Handbook of Categorical Algebra: Volume 2, Categories and Structures PDF Download
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Author: Francis Borceux
Publisher: Cambridge University Press
ISBN: 052144179X
Category : Mathematics
Languages : en
Pages : 470
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Book Description
The Handbook of Categorical Algebra is designed to give, in three volumes, a detailed account of what should be known by everybody working in, or using, category theory. As such it will be a unique reference. The volumes are written in sequence. The second, which assumes familiarity with the material in the first, introduces important classes of categories that have played a fundamental role in the subject's development and applications. In addition, after several chapters discussing specific categories, the book develops all the major concepts concerning Benabou's ideas of fibred categories. There is ample material here for a graduate course in category theory, and the book should also serve as a reference for users.
Author: Francis Borceux
Publisher: Cambridge University Press
ISBN: 052144179X
Category : Mathematics
Languages : en
Pages : 470
Get Book
Book Description
The Handbook of Categorical Algebra is designed to give, in three volumes, a detailed account of what should be known by everybody working in, or using, category theory. As such it will be a unique reference. The volumes are written in sequence. The second, which assumes familiarity with the material in the first, introduces important classes of categories that have played a fundamental role in the subject's development and applications. In addition, after several chapters discussing specific categories, the book develops all the major concepts concerning Benabou's ideas of fibred categories. There is ample material here for a graduate course in category theory, and the book should also serve as a reference for users.
Author: Francis Borceux
Publisher: Cambridge University Press
ISBN: 9780521061223
Category : Mathematics
Languages : en
Pages : 0
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Book Description
The second volume, which assumes familiarity with the material in the first, introduces important classes of categories that have played a fundamental role in the subject's development and applications. In addition, after several chapters discussing specific categories, the book develops all the major concepts concerning Benabou's ideas of fibered categories.
Author: Francis Borceux
Publisher: Cambridge University Press
ISBN: 9780521061193
Category : Mathematics
Languages : en
Pages : 0
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Book Description
A Handbook of Categorical Algebra, in three volumes, is a detailed account of everything a mathematician needs to know about category theory. Each volume is self-contained and is accessible to graduate students with a good background in mathematics. Volume 1 is devoted to general concepts. After introducing the terminology and proving the fundamental results concerning limits, adjoint functors and Kan extensions, the categories of fractions are studied in detail; special consideration is paid to the case of localizations. The remainder of the first volume studies various "refinements" of the fundamental concepts of category and functor.
Author: Francis Borceux
Publisher:
ISBN:
Category : Abelian categories
Languages : en
Pages : 472
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Book Description
Author: Francis Borceux
Publisher: Cambridge University Press
ISBN: 0521441781
Category : Mathematics
Languages : en
Pages : 363
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Book Description
The Handbook of Categorical Algebra is designed to give, in three volumes, a detailed account of what should be known by everybody working in, or using, category theory. As such it will be a unique reference. The volumes are written in sequence, with the first being essentially self-contained, and are accessible to graduate students with a good background in mathematics. In particular, Volume 1, which is devoted to general concepts, can be used for advanced undergraduate courses on category theory.
Author: Francis Borceux
Publisher:
ISBN: 9781107383753
Category : Categories (Mathematics)
Languages : en
Pages : 443
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Book Description
Second in a three part set, this volume introduces important classes of categories (abelian, monadic, fibred, etc.).
Author: Francis Borceux
Publisher: Cambridge University Press
ISBN: 0521441803
Category : Mathematics
Languages : en
Pages : 544
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Book Description
The Handbook of Categorical Algebra is intended to give, in three volumes, a rather detailed account of what, ideally, everybody working in category theory should know, whatever the specific topic of research they have chosen. The book is planned also to serve as a reference book for both specialists in the field and all those using category theory as a tool. Volume 3 begins with the essential aspects of the theory of locales, proceeding to a study in chapter 2 of the sheaves on a locale and on a topological space, in their various equivalent presentations: functors, etale maps or W-sets. Next, this situation is generalized to the case of sheaves on a site and the corresponding notion of Grothendieck topos is introduced. Chapter 4 relates the theory of Grothendieck toposes with that of accessible categories and sketches, by proving the existence of a classifying topos for all coherent theories.
Author: Juliette Kennedy
Publisher: Springer
ISBN: 3662553864
Category : Mathematics
Languages : en
Pages : 401
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Book Description
Edited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the 24th Workshop on Logic, Language, Information and Communication, WoLLIC 2017, held in London, UK, in August 2017. The 28 contributed papers were carefully reviewed and selected from 61 submissions. They cover interdisciplinary research in pure and applied logic, aiming at interactions between logic and the sciences related to information and computation.
Author: Saunders Mac Lane
Publisher: Springer Science & Business Media
ISBN: 1475747217
Category : Mathematics
Languages : en
Pages : 320
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Book Description
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. It 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 characterised by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.
Author: Francis Borceux
Publisher:
ISBN: 9781107094673
Category : Categories (Mathematics)
Languages : en
Pages : 363
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Book Description
First of a 3-volume work giving a detailed account of what should be known by all working in, or using category theory. Volume 1 covers basic concepts.
