$18.20 (33% off) Basic Category Theory $55.96 (25% off) Categories for the Working $34.97 (30% off) Sets, Logic and Categories $99.20 (20% off) Categorical Logic and $47.69 (13% off) Category Theory $179.00 The Theory of Categories $59.96 (25% off) Measure and Category $50.04 Accessible Categories $118.55 (20% off) Tool and Object $100.00 Categories and Computer

1. Basic Category Theory for Computer Scientists (Foundations of Computing) by Benjamin C. Pierce List Price: Price: You Save: US$27.00 US$18.20 US$8.8 (33%) Category: Paperback (1991-08-07) Publisher: The MIT Press ISBN: 0262660717 Sales Rank: 270534 Lowest New Price: $18.20 Lowest Used Price: $11.00 (20 Used Items) Canada | United Kingdom | Germany | France | Japan Product Description Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse. Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts. Contents: Tutorial. Applications. Further Reading. ... Read more Features: ISBN13: 9780262660716 Condition: New Notes: BUY WITH CONFIDENCE, Over one million books sold! 98% Positive feedback. Compare our books, prices and service to the competition. 100% Satisfaction Guaranteed Customer Reviews Average Customer Review: Based on 7 reviews. A Good Read This book is not exactly what I would call easy going. I've managed to get through half of it in 7 months. However, I can say, with absolute confidence, that if you do the problems you will learn. Most everything I've seen on category theory is a confusing mixture of different notations with seemingly identical meanings (but in fact the meanings are totally different). This book is no exception. Often, I have resorted to IRC to sort things out when some notation is simply impenetrable to me. My mathematical training stopped at complex calculus, so this may not apply to you if you've had abstract algebra or something a little more 'meta'. There seems to be one typographical error, but I am not sure. In the example on the adjunction between products and exponentiation, the right adjoint is listed as "(_)^A x A" but in the diagrams it ends up as "(_)^A". This may be a sensible ellision, but it is not explained anywhere in the text and of it's not easy to find these things on the internet. Good Introduction I have been reading several different category theory texts recently, and this one was very succinct and accessible. Particularly useful for understanding functional programming. Basic crib sheet for category theory Anyone coming to this book from Pierce's "Types and Programming Languages" will be disappointed. While his "Types ..." book is a model of clear exposition, this book reads like a set of notes jotted down on the back on an envelope. The extensive bibliographic sections are more than fifteen years out of date. Much of the material referenced is no longer in print, and recent developments are, of course, not mentioned. Those seeking a very gentle introduction to category theory would do better with the book by Lawvere and Schanuel, who cover more of category theory than Pierce. Mathematically mature computer science readers will find everything they need to know about the subject in Mac Lane's book. Really expensive for a set of notes... You can find better introductions to category theory available on the net for free. Try searching for Lambert Meertens, Marten Fokkinga, and Jaap Van Oosten, for example. Or Barr and Wells, Triples, Toposes, and Theories. Or Asperti and Longo. Or watch Eugenia Cheng's videos on YouTube, which are fantastic. But if you want to buy a book, get Barr and Wells, Category Theory for Computing Science. Unfortunately, you have to order it directly from the University of Montreal. It's a great book, by far the best intro to category theory available, *way* better than this! Then, after that, you can read MacLane... Too terse This is a very short book: 70 pages of text + a bibliography. The first 50 pages are about general category theory, and the last 20 pages are specifically for computer scientists. My interest is in general category theory, and I bought this because I have a BS in CS and thought I'd find plenty of familiar examples. Unfortunately this book doesn't have nearly enough examples. I found it easier to skim some undergrad abstract algebra books in the library (groups, rings, vector spaces) and then continuing with category theory intros written for math students. ... Read more Similar Items: 1. Types and Programming Languages 2. Purely Functional Data Structures 3. Advanced Topics in Types and Programming Languages 4. The Haskell Road to Logic, Maths and Programming (Texts in Computing) 5. Conceptual Mathematics: A First Introduction to Categories . Favourite Lists: 1. Zealot's List of Computer Science, Operating System and Compiler Books. 2. Basic (language agnostic) programmer's references. 3. Programming Language Research Books. 4. category/topos theory (i.e. math foundations).

2. Categories for the Working Mathematician (Graduate Texts in Mathematics) by Saunders Mac Lane List Price: Price: You Save: US$74.95 US$55.96 US$18.99 (25%) Category: Hardcover (1998-09-25) Publisher: Springer ISBN: 0387984038 Sales Rank: 131444 Lowest New Price: $55.21 Lowest Used Price: $55.21 (16 Used Items) Canada | United Kingdom | Germany | France | Japan Product Description Categories for the Working Mathematician provides an array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. The book then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterized by Beck's theorem. After considering a variety of applications, the book continues with the construction and expoitation of Kan extensions. This second edition includes a number of revisions and additions, including two new chapters on topics of active interest. One is on symmetric monoidal categories and braided monoidal categories and the coherence theorems for them. The second describes 2-categories and the higher dimensional categories which have recently come into prominence. The bibliography has also been expanded to cover some of the many other recent advances concerning categories. ... Read more Customer Reviews Average Customer Review: Based on 8 reviews. Simply Great Have you ever tried reading Descartes' "Geometry"? It's not a good place to learn about coordinate geometry. I tried. This was almost 10 years ago, but I still remember it pretty well. Ok, so maybe the experience was even a bit traumatic. Usually when someone works out a theory, it takes a fresh perspective (or two, or ... you get it) to really digest it, and come up with a reasonable way of teaching it to newcomers. It's less evident nowadays, with improved communications technology and such, but people aren't exactly turning to Grothendieck's expositions as their intro to his geometry either. Mac Lane is an exception. This book seems completely inapproachable. The title is scary. The topic is scary. Open to a random page and try to judge its accessibility: scary. Well, here's the real story: you need to know algebra through modules, and it'd be nice if this algebra background introduced "universals" like abelianization or free modules in a way that involved the diagrams and the unique mappings you get from the given ones. If this stuff makes any sense, you can read this book. It's not that scary. If you're up to the challenge, you might even enjoy it. This is actually my favorite book. Here's the approach that I feel worked well for me: - gloss over the set-theoretic foundations at first. Make sure you know the proper class/set and large/small category distinctions, but don't dwell on them much. - focus on the examples that are familiar, but read through the others too. Mac Lane uses tons of examples to suit a variety of backgrounds, and his presentation is so clear that the theory can often explain the examples. - trust the author. It may seem like product or comma categories deserve fuller treatment with more motivation. No. Let Mac Lane's 'minimalism' infect your thinking: it's no more complicated than what's on those pages. Make sure you *know* what's there, and you will come to *understand* the material as it is fleshed out through exercises or later writing. The last point has been the most important for me. This book has been a great lesson in clear thinking, which is of extreme importance in mathematics. Why? It's complicated enough! Poorly written standard text. This book has everything you need, but it is written in an abstruse style in my opinion. A Classic Well, let us think about this a little bit...You want to learn Category theory, whether for some course or just for the fun of it, and now where do you turn in order to learn the necessary concepts. If you are a mathematician and have some experience, then you turn to the masters, the originators of the given subject and read their work. Sure, being the founder of a given subject does not imply that you are a good expositor and hence are capable of revealing the necessary concepts for the beginner-allow me to inform that Mac Lane is indeed as good as an expositor as he was a mathematician. For any doubters, I point you to the only other text you should read on Category theory, namely, "Category Theory" by Horst Herrlich and compare this text with Mac Lane's. Aside from that, and with respect to the text, for most beginners or interested readers I would suggest the following outline: Read 1.1-6; 2.1-3 & 8 possibly 2.4; all of 3; as for 4 skip section 3; 5.1-5; all of 8. Then, dependent upon your desires and or focus as well as your mathematical ability, it should become obvious which of the remaining topics should be read. Finally, the only other source I would recommend for learning Category theory can be found on-line using the keyword 'Awodey'. Anyways, Enjoy and good luck. You may not need this unless you major in category theory. I entirely agree with the reviewer Lucas Wilman. As a book by the creator of category theory, it has extensively incorpoated relevant items. However I don't think this is a *must read" unless you major in the subject: you will seldom need more than what is covered in a typical homological algebra course. My inmpression is this book should be entitled "Categories for the starting/working category theorists". Classic and worth it It is difficult to make understand what "is" category theory. Is it a foundational discipline? Is it a discipline studying homomorphisms between algebras? Is it nonsense? Well, in my opinion this book does not help in gaining this kind of understanding. But all the stuff I read which have been written with that purpose in mind did not have any success - perhaps because I am not a mathematician, or perhaps because some concepts in category theory are really too abstract for anyone to give "an intuition" of them (you still can with functors and natural transformations, but try with adjointness...). This said, I found the book wonderful: Every concept is presented neatly. I use it as a reference each time I want a clear and rigorous definition of a concept. Sometimes this rigour helped me in gaining the famous intuition behind the concept. ... Read more Similar Items: 1. Topoi: The Categorial Analysis of Logic (Dover Books on Mathematics) 2. Conceptual Mathematics: A First Introduction to Categories 3. An Introduction to Homological Algebra (Cambridge Studies in Advanced Mathematics) 4. Set Theory and the Continuum Hypothesis (Dover Books on Mathematics) 5. Algebraic Geometry (Graduate Texts in Mathematics) . Favourite Lists: 1. Category Theory. 2. Books Mathematicians Should Read. 3. A Good Collection of Math Texts. 4. about postmodern philosophy. 5. Classics in Algebra. 6. background resources for constructing an epistemology. 7. category/topos theory (i.e. math foundations). 8. Rediscover thought processes in Computer Science.

3. Sets, Logic and Categories (Springer Undergraduate Mathematics Series) by Peter J. Cameron List Price: Price: You Save: US$49.95 US$34.97 US$14.98 (30%) Category: Paperback (1999-03-05) Publisher: Springer ISBN: 1852330562 Sales Rank: 873591 Lowest New Price: $29.36 Lowest Used Price: $15.00 (12 Used Items) Canada | United Kingdom | Germany | France | Japan Product Description Set theory, logic and category theory lie at the foundations of mathematics, and have a dramatic effect on the mathematics that we do, through the Axiom of Choice, Gödel's Theorem, and the Skolem Paradox. But they are also rich mathematical theories in their own right, contributing techniques and results to working mathematicians such as the Compactness Theorem and module categories. The book is aimed at those who know some mathematics and want to know more about its building blocks. Set theory is first treated naively an axiomatic treatment is given after the basics of first-order logic have been introduced. The discussion is supported by a wide range of exercises. The final chapter touches on philosophical issues. The book is supported by a World Wide Web site containing a variety of supplementary material. ... Read more Customer Reviews Average Customer Review: Based on 1 reviews. Poor refrence/class textbook. Good preview, general overview for selected topics in FOM Having purchased this text (as part of the Springer Undergraduate Mathematics Series), I expected a decent publication. I had purchased and used their Number Theory text (Jones & Jones) and I was satisfied with the overal quality of the problem sets and the exposition. Like all the SUMS texts, this book provides the solutions (in this case selected solutions and the link to the website that has the rest) for all the excercises found in this textbook. However, in this case, the excercises are much to trivial to be considered a good workout in any of the topics covered in this book. To account briefly book covers Naive Set Theory, Sentential Logic, 1st Order Predicate Calculus, "Model Theory" (I'll explain the quote later), Ordinal numbers, Aximoatic Set Theory, and Category Theory. Topics that are missing in a introductory treatment includes Recursion Theory, most of even the basic developments of Model Theory. This would be fine in it of itself, however, what the text does cover, namely the 1st order Predicate Caculus and Model Theory, is so sparing that one gets a very tiny glimpse of the subject and that is it. For a SUMS text, the book is suprisingly lacking in rigor and substance. Theorems are still stated and proved yet nothing but the most basic results are displayed. For instance, in 1st order predicate calculus the book introduces the Deduction theorem then right after goes to Soundness and then Completeness. It seems the topics of symbol substitutibility, Henkin langauge expansion, and quantifier elemination were totally ommited. These are very important topics, topics no introduction to Mathematical logic should be without, yet they are absent in this text. Further, the chapter on Model Theory is nothing but theorem throwing at the reader. In the 2nd page and little bit after, the reader is introduced to Lowenheim-Skolem Theorem, Compactness, Consistency and a very brief expostion on a Peano Arithemtic system. This chapter also serves as a brief introduction to incompleteness (perhaps a page introduction at most). But to be honest, even the proofs given for these thoerems are lacking and wouldn't satisfy many students of this subject as a suffecient explanation (let alone a potential refrence). To demonstrate the unbelievable terseness (and sheer lacking) of this exposition, the book discusses everything on Godel numbers to incompleteness in a span of 3 - 4 pages. Even in "light" introductions, such as Enderton, this development and the accompanying machinary requires an entire chapter to develop (and Cameron has ommited a signifcent amount of the machianry by ommited all of Recursion theory). The good in this book or perhaps more accurately, the unqiue, are that it does give an introduction to ordinals (usually reserved for Intro. Set Theory books) and a light introduction to Category Theory ("preview" is more fitting for that chapter). In fact, "Preview" is a very fitting description of this textbook in general. This text cannot hope to serve as anything more then a preview for the subject discussed within those pages. People who wish to develop a working knowledge of this subject should look towards Enderton as a "lighter" introduction (if Enderton is a diet Coke, then this book is certainly water). I think this text would go well in two scenarios. One, a indivudal who is about to take his firs FOM course and uses this book as a preview durring the summer (or Winter break) before actually taking the course. The second scenario would be to use this text as a followup with Springer's other text Johnson's "Elements of Logic via Numbers and Sets." That text combined with this would serve as a very good "bridge" course to abstract mathematics. If, however, you are not one of the above mentioned, then I recommend that you consider purchsing one of hte other more establisehd text on Mathematical logic as this book is to light (and in my opinoin to expensive for the amount of material given) to serve as a useful text. Thus, this book may fail totatlly as a textbook for a intro. FOM course, however it can still find some use as a advanced preview for the subject or a companion in a abstract matheamtics bridge course. ... Read more Similar Items: 1. Metric Spaces (Springer Undergraduate Mathematics Series) 2. Analytic Methods for Partial Differential Equations (Springer Undergraduate Mathematics Series) 3. Numerical Methods for Partial Differential Equations 4. An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics) 5. Elementary Differential Geometry (Springer Undergraduate Mathematics Series) . Favourite Lists: 1. Springer Undergraduate Mathematics Series. 2. Good Math Books.

4. Categorical Logic and Type Theory, Volume 141 (Studies in Logic and the Foundations of Mathematics) by B. Jacobs List Price: Price: You Save: US$124.00 US$99.20 US$24.8 (20%) Category: Hardcover (2001-05-24) Publisher: Elsevier Science ISBN: 0444508538 Sales Rank: 1951036 Lowest New Price: $99.20 Lowest Used Price: $144.49 (3 Used Items) Canada | United Kingdom | Germany | France | Japan Product Description This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists. ... Read more Customer Reviews Average Customer Review: Based on 1 reviews. Excellent book. Excellent book. The best in its field. I would recommend it, particularly for students. ... Read more Similar Items: 1. First Order Categorical Logic: Model-Theoretical Methods in the Theory of Topoi and Related Categories (Lecture Notes in Mathematics) 2. Introduction to Higher-Order Categorical Logic (Cambridge Studies in Advanced Mathematics) 3. Lecture Notes on Topoi and Quasitopoi .

5. Category Theory (Oxford Logic Guides) by Steve Awodey List Price: Price: You Save: US$55.00 US$47.69 US$7.31 (13%) Category: Paperback (2010-08-13) Publisher: Oxford University Press, USA ISBN: 0199237182 Sales Rank: 467768 Lowest New Price: $42.06 Lowest Used Price: $42.04 (8 Used Items) Canada | United Kingdom | Germany | France | Japan Product Description Category theory is a branch of abstract algebra with incredibly diverse applications. This text and reference book is aimed not only at mathematicians, but also researchers and students of computer science, logic, linguistics, cognitive science, philosophy, and any of the other fields in which the ideas are being applied. Containing clear definitions of the essential concepts, illuminated with numerous accessible examples, and providing full proofs of all important propositions and theorems, this book aims to make the basic ideas, theorems, and methods of category theory understandable to this broad readership. Although assuming few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda's lemma; adjoints; monads. An extra topic of cartesian closed categories and the lambda-calculus is also provided - a must for computer scientists, logicians and linguists! This Second Edition contains numerous revisions to the original text, including expanding the exposition, revising and elaborating the proofs, providing additional diagrams, correcting typographical errors and, finally, adding an entirely new section on monoidal categories. Nearly a hundred new exercises have also been added, many with solutions, to make the book more useful as a course text and for self-study. ... Read more Customer Reviews Average Customer Review: Based on 1 reviews. It's the glue. Several years ago I came across an on-line .pdf format of Awodey's manuscript while trying to find a text on Category Theory whose content was not as intense as Mac Lane's `Categories for the Working Mathematician' and it is wonderful to see this book come to fruition. Without a doubt it is true that the available array of Category theoretic texts for mathematicians has been confined to the more abstract texts whose readership is limited to those individuals who are either researching topics integral to Category theory or graduate students of, say Algebraic Topology/Geometry, who utilize Categorical constructs and processes within the confines of their respective fields. So where does this text fit in? I believe this text can be quantified as "the glue" between Category theoretic texts written for non-mathematicians and the hardcore texts of Mac Lane, Herrlich or Ademek et al. What features set this text apart from the others? Simple, it is focused. Let me preface my explanation with the following: I firmly believe in the importance of demonstrating or motivating any given subject through the use of concrete examples and, in particular, through the use of several examples that can be built upon throughout the text. Awodey sees the importance of this and focuses on illuminating the abstractness of Category theory by carefully building on or utilizing Monoids and Posets. Such structures may readily seem un-familiar to some readers but, if they pause long enough to compare what they know with the basic axioms for a given set to be a Monoid/Poset, then they will see that the majority of structures in which they have been working are, in fact, specialized Monoids/Posets. Take for example Groups. Any set possessing an associative binary law of composition all of whose objects satisfy the 3-axioms for a group also trivially satisfy the axioms for a Monoid. This is not to say that Awodey has chosen two basic blocks from which all examples are derived, instead, he motivates each topic with a vast assortment of the standard examples taken from a diverse set of available fields. So who should read this text? Anyone who wants to learn Category Theory from the ground up but lacks the standard assumed breadth of knowledge, namely, familiarity with Topology, in particular Algebraic Topology, as well as advanced abstract Algebra (inclusive of Module theory). As in any case of defining the readership one would state that their text is readable by the illusive and readily undefined "mathematically mature" student. Personally I would assume that you know how construct logically sound proofs and that you have taken courses in set theory (never given in America) as well as Algebra at the level of, say Hungerford's undergraduate text. Furthermore, and as is the case with anything mathematical, you must be willing to suffer through abstractness and be diligent as well as disciplined enough to work through the exercises. With respect to this last point, Awodey does a remarkable job providing a well thought out set of exercises ranging from simple applications of the material to more advanced exercises that will cause you to pull out your hair and possibly throw the book across the room in sheer agony. As a final note regarding the overall text, I would even suggest this Awodey's book to more advanced student who lack a firm understanding of Category Theory but who have already suffered through someone else's text. Why? Simple, because Awodey's text will help you `see' and hence understand, at the necessary level, Category Theory. After all, one can not become proficient in anything unless they `see' what it is they are trying to become proficient in. Finally, I would like to personally thank Mr. Awodey for writing this text and for doing such a remarkable job introducing and motivating a miraculous and awe-inspiring subject. Enjoy! ... Read more Similar Items: 1. Conceptual Mathematics: A First Introduction to Categories 2. Categories for the Working Mathematician (Graduate Texts in Mathematics) 3. Topoi: The Categorial Analysis of Logic (Dover Books on Mathematics) 4. Algebra: Chapter 0 (Graduate Studies in Mathematics) 5. Abstract and Concrete Categories: The Joy of Cats .

6. The Theory of Categories (Nijhoff International Philosophy Series) by F.C. Brentano List Price: Price: US$179.00 US$179.00 Category: Hardcover (1981-02-28) Publisher: Springer ISBN: 9024723027 Sales Rank: 4409942 Lowest New Price: $169.30 Lowest Used Price: $155.74 (5 Used Items) Canada | United Kingdom | Germany | France | Japan

7. Measure and Category: A Survey of the Analogies between Topological and Measure Spaces (Graduate Texts in Mathematics) by John C. Oxtoby List Price: Price: You Save: US$79.95 US$59.96 US$19.99 (25%) Category: Hardcover (1980-09-29) Publisher: Springer ISBN: 0387905081 Sales Rank: 789290 Lowest New Price: $59.96 Lowest Used Price: $63.97 (12 Used Items) Canada | United Kingdom | Germany | France | Japan Customer Reviews Average Customer Review: Based on 2 reviews. Good classical book This is a book first published in the 70's and it has the advantage of being easy reading and short. It presents to the student with little background (a course of real analysis or calculus is all that is required, together with some familiarity with set theoretic reasoning) some of the classical and powerful results of measure and set theory and analysis in an elegant and modern way. It explores in a diversity of ways the analogies of measure and category and the uses of Baire and Borel's theorems. I believe it is one of the best introductions of measure theory that can be found in the literature. Interesting monograph on measure theory This short book is an interesting account of measure theory and how it relates to topology. The topics are the standard ones that one would find in a book on the subject, and the book is a real pleasure to read. Its length motivates one to finish the book and the book is very applicable to the theory of dynamical systems and the theory of large deviations. It could be used as a textbook on measure theory or foundations of analysis if one supplemented it with problem sets and some outside reading. A good book. ... Read more Similar Items: 1. Algebra 2. Categories for the Working Mathematician (Graduate Texts in Mathematics) 3. Counterexamples in Topology 4. A Course in Functional Analysis 5. Real and Complex Analysis (International Series in Pure and Applied Mathematics) .

8. Accessible Categories: The Foundations of Categorical Model Theory (Contemporary Mathematics) by Michael Makkai, Robert Pare List Price: $40.00 Category: Paperback (1989-12) Publisher: Amer Mathematical Society ISBN: 082185111X Sales Rank: 1356917 Lowest New Price: $50.04 Lowest Used Price: $85.98 (3 Used Items) Canada | United Kingdom | Germany | France | Japan Product Description Intended for category theorists and logicians familiar with basic category theory, this book focuses on categorical model theory, which is concerned with the categories of models of infinitary first order theories, called accessible categories. The starting point is a characterization of accessible categories in terms of concepts familiar from Gabriel-Ulmer's theory of locally presentable categories. Most of the work centers on various constructions (such as weighted bilimits and lax colimits), which, when performed on accessible categories, yield new accessible categories. These constructions are necessarily 2-categorical in nature; the authors cover some aspects of 2-category theory, in addition to some basic model theory, and some set theory. One of the main tools used in this study is the theory of mixed sketches, which the authors specialize to give concrete results about model theory. Many examples illustrate the extent of applicability of these concepts. In particular, some applications to topos theory are given. Perhaps the book's most significant contribution is the way it sets model theory in categorical terms, opening the door for further work along these lines. Requiring a basic background in category theory, this book will provide readers with an understanding of model theory in categorical terms, familiarity with 2-categorical methods, and a useful tool for studying toposes and other categories. ... Read more

9. Tool and Object: A History and Philosophy of Category Theory (Science Networks. Historical Studies) by Ralf Krömer List Price: Price: You Save: US$149.00 US$118.55 US$30.45 (20%) Category: Hardcover (2007-03-28) Publisher: Birkhäuser Basel ISBN: 376437523X Sales Rank: 711581 Lowest New Price: $101.51 Lowest Used Price: $89.95 (10 Used Items) Canada | United Kingdom | Germany | France | Japan Product Description Category theory is a general mathematical theory of structures and of structures of structures. It occupied a central position in contemporary mathematics as well as computer science. This book describes the history of category theory whereby illuminating its symbiotic relationship to algebraic topology, homological algebra, algebraic geometry and mathematical logic and elaboratively develops the connections with the epistemological significance. ... Read more Customer Reviews Average Customer Review: Based on 1 reviews. Review of Krömer's Tool and Object The main goal of the book under review is to provide a systematic and profound analysis of several important historical and epistemological aspects of category theory. The central theme of the book is to give an analysis of the remarkable fact that category theory gained position in daily mathematics as a useful and legitimate conceptual innovation, in spite of the difficulties of its set-theoretical foundations and the challenge it caused to this formerly well-established mathematical foundation and to some epistemological positions. The philosophical stance to category theory developed here is inspired by the pragmatism of Peirce and by Wittgenstein's criticisms of reductionism, which represents a highly interesting alternative to more traditional approaches in philosophy of mathematics like logicism, intuitionism, formalism, realism, fictionalism, etc. In this vein, the author's philosophical position focusses on the "use" of concepts, instead of formal syntax and semantics, and on the thesis that that philosophical justification of mathematical reasoning is an accurate description of the way mathematicians work with categories. I missed, in the context of a philosophy of category theory, more detailed discussions on some category-theorists philosophical positions, like Lawvere's "dialectical" philosophy of mathematics, different versions of structuralism and different "topos foundations" (for instance, those of Lambek, Bell, Mac Lane) and in this sense the book is more a history than a philosophy of category theory. Some passages are obscured rather than clarified by the philosophical tone, and a methodological fault is that the author sometimes regards spontaneous declarations of some mathematicians as well-elaborated philosophical conceptions or official historical explanations. Nonetheless, this work is a serious attempt to discuss the history and a philosophy of category theory, and historians of mathematics, philosophers of mathematics, and also "working" mathematicians can profit to a large extent from Krömer's analysis. ... Read more Similar Items: 1. What is Category Theory? 2. Abstract and Concrete Categories: The Joy of Cats 3. From a Geometrical Point of View: A Study of the History and Philosophy of Category Theory (Logic, Epistemology, and the Unity of Science) 4. Handbook of Practical Logic and Automated Reasoning 5. Set Theory and the Continuum Hypothesis (Dover Books on Mathematics) . Favourite Lists: 1. Category Theory. 2. The History of Philosophy and Logic. 3. Scholarly Histories of Mathematical Disciplines.

10. Categories and Computer Science (Cambridge Computer Science Texts) by R. F. C. Walters List Price: Price: US$100.00 US$100.00 Category: Hardcover (1992-08-28) Publisher: Cambridge University Press ISBN: 0521419972 Sales Rank: 4799495 Lowest New Price: $95.71 Lowest Used Price: $61.19 (8 Used Items) Canada | United Kingdom | Germany | France | Japan Product Description Category Theory has, in recent years, become increasingly important and popular in computer science, and many universities now introduce Category Theory as part of the curriculum for undergraduate computer science students. Here, the theory is developed in a straightforward way, and is enriched with many examples from computer science. ... Read more Customer Reviews Average Customer Review: Based on 2 reviews. a recommendation of Category Theory texts for CS/IT In September 1997 we needed a book on Category Theory for our first year undergraduate class in the B.A. (Mod) honors degree in Information and Communications Technology (ICT) at the University of Dublin, Trinity College, Dublin 2, Ireland. This book was at that time the only one that satisfied our requirements. Now we have chosen (Lawvere and Schanuel 1997) in addition. It is our opinion that one ought to start with the latter, a most excellent introduction of great profundity, and, for application to computing, use the Walters text. It is hard to beat this combination for a first year undergraduate course, as far as we know at this time (Sept.98) A Very comprehensive textbook for beginners computer sci. The Book begins with the plain definition of a category, as does any other book. However, it points out a category as a kind of (abstract) Data Type. Distributive Categories are discussed as a milestone for developing the basic concepts in computation, as those of imperative programs and Data Types. The Book has a lot of examples (from computation) and the author took care of drawning conclusions from them before develop an abstract framework. The concepts of automata and automata with inputs are shown (the later in a functorial category). Grammars and Graphs are discussed as well. The book has a very good introduction to the concept of freeness and adjunctions. Its latest chapter treats the computational category theory in the context of Knuth-Bendix procedure. The exercises present in the book are great !! They guide the student gradualy into deeper questions without any frustation. There are very easy exercises which have the only goal of finding out ones undersating of a new definition. ... Read more Similar Items: 1. Conceptual Mathematics: A First Introduction to Categories 2. Basic Category Theory for Computer Scientists (Foundations of Computing) 3. Categories for Types (Cambridge Mathematical Textbooks) 4. Types and Programming Languages 5. Category Theory (Oxford Logic Guides) .