Handbook Of Categorical Algebra Volume 2 Categories And Structures

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Handbook of Categorical Algebra: Volume 2, Categories and Structures

Francis Borceux
Handbook of Categorical Algebra Volume 2 Categories and Structures Book PDF

Author : Francis Borceux
Publisher : Cambridge University Press
Page : 470 pages
File Size : 52,8 Mb
Release : 1994-11-03
Category : Mathematics
ISBN : 9780521441797

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Handbook of Categorical Algebra: Volume 2, Categories and Structures by Francis Borceux Pdf

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.

Handbook of Categorical Algebra: Volume 2, Categories and Structures

Francis Borceux
Handbook of Categorical Algebra Volume 2 Categories and Structures Book PDF

Author : Francis Borceux
Publisher : Cambridge University Press
Page : 0 pages
File Size : 42,6 Mb
Release : 2008-04-24
Category : Mathematics
ISBN : 0521061229

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Handbook of Categorical Algebra: Volume 2, Categories and Structures by Francis Borceux Pdf

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.

Handbook of Categorical Algebra 2

Francis Borceux
Handbook of Categorical Algebra 2 Book PDF

Author : Francis Borceux
Publisher : Unknown
Page : 443 pages
File Size : 46,5 Mb
Release : 1994
Category : Abelian categories
ISBN : 1139881973

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Handbook of Categorical Algebra 2 by Francis Borceux Pdf

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.

Handbook of Categorical Algebra: Volume 1, Basic Category Theory

Francis Borceux
Handbook of Categorical Algebra Volume 1 Basic Category Theory Book PDF

Author : Francis Borceux
Publisher : Cambridge University Press
Page : 0 pages
File Size : 41,6 Mb
Release : 2008-04-24
Category : Mathematics
ISBN : 0521061199

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Handbook of Categorical Algebra: Volume 1, Basic Category Theory by Francis Borceux Pdf

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.

Handbook of Categorical Algebra: Volume 1, Basic Category Theory

Francis Borceux
Handbook of Categorical Algebra Volume 1 Basic Category Theory Book PDF

Author : Francis Borceux
Publisher : Cambridge University Press
Page : 363 pages
File Size : 51,6 Mb
Release : 1994-08-26
Category : Mathematics
ISBN : 9780521441780

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Handbook of Categorical Algebra: Volume 1, Basic Category Theory by Francis Borceux Pdf

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.

Handbook of Categorical Algebra

Francis Borceux
Handbook of Categorical Algebra Book PDF

Author : Francis Borceux
Publisher : Unknown
Page : 443 pages
File Size : 49,6 Mb
Release : 1994
Category : Categories (Mathematics)
ISBN : 1107383757

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Handbook of Categorical Algebra by Francis Borceux Pdf

Second in a three part set, this volume introduces important classes of categories (abelian, monadic, fibred, etc.).

Handbook of Categorical Algebra: Volume 1, Basic Category Theory

Francis Borceux
Handbook of Categorical Algebra Volume 1 Basic Category Theory Book PDF

Author : Francis Borceux
Publisher : Cambridge University Press
Page : 0 pages
File Size : 40,8 Mb
Release : 2008-04-24
Category : Mathematics
ISBN : 0521061199

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Handbook of Categorical Algebra: Volume 1, Basic Category Theory by Francis Borceux Pdf

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.

Handbook of Categorical Algebra: Volume 3, Sheaf Theory

Francis Borceux
Handbook of Categorical Algebra Volume 3 Sheaf Theory Book PDF

Author : Francis Borceux
Publisher : Cambridge University Press
Page : 544 pages
File Size : 41,9 Mb
Release : 1994-12-08
Category : Mathematics
ISBN : 9780521441803

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Handbook of Categorical Algebra: Volume 3, Sheaf Theory by Francis Borceux Pdf

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.

Logic, Language, Information, and Computation

Juliette Kennedy,Ruy J.G.B. de Queiroz
Logic Language Information and Computation Book PDF

Author : Juliette Kennedy,Ruy J.G.B. de Queiroz
Publisher : Springer
Page : 401 pages
File Size : 55,9 Mb
Release : 2017-07-10
Category : Mathematics
ISBN : 9783662553862

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Logic, Language, Information, and Computation by Juliette Kennedy,Ruy J.G.B. de Queiroz Pdf

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.

Categories for the Working Mathematician

Saunders Mac Lane
Categories for the Working Mathematician Book PDF

Author : Saunders Mac Lane
Publisher : Springer Science & Business Media
Page : 320 pages
File Size : 40,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475747218

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Categories for the Working Mathematician by Saunders Mac Lane Pdf

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.

Handbook of Algebra

Anonim
Handbook of Algebra Book PDF

Author : Anonim
Publisher : Elsevier
Page : 936 pages
File Size : 53,9 Mb
Release : 1995-12-18
Category : Mathematics
ISBN : 9780080532950

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Handbook of Algebra by Anonim Pdf

Handbook of Algebra defines algebra as consisting of many different ideas, concepts and results. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. Each chapter of the book combines some of the features of both a graduate-level textbook and a research-level survey. This book is divided into eight sections. Section 1A focuses on linear algebra and discusses such concepts as matrix functions and equations and random matrices. Section 1B cover linear dependence and discusses matroids. Section 1D focuses on fields, Galois Theory, and algebraic number theory. Section 1F tackles generalizations of fields and related objects. Section 2A focuses on category theory, including the topos theory and categorical structures. Section 2B discusses homological algebra, cohomology, and cohomological methods in algebra. Section 3A focuses on commutative rings and algebras. Finally, Section 3B focuses on associative rings and algebras. This book will be of interest to mathematicians, logicians, and computer scientists.

2-Dimensional Categories

Niles Johnson,Donald Yau
2 Dimensional Categories Book PDF

Author : Niles Johnson,Donald Yau
Publisher : Oxford University Press
Page : 476 pages
File Size : 40,9 Mb
Release : 2021-01-31
Category : Science
ISBN : 9780192645678

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2-Dimensional Categories by Niles Johnson,Donald Yau Pdf

Category theory emerged in the 1940s in the work of Samuel Eilenberg and Saunders Mac Lane. It describes relationships between mathematical structures. Outside of pure mathematics, category theory is an important tool in physics, computer science, linguistics, and a quickly-growing list of other sciences. This book is about 2-dimensional categories, which add an extra dimension of richness and complexity to category theory. 2-Dimensional Categories is an introduction to 2-categories and bicategories, assuming only the most elementary aspects of category theory. A review of basic category theory is followed by a systematic discussion of 2-/bicategories, pasting diagrams, lax functors, 2-/bilimits, the Duskin nerve, 2-nerve, internal adjunctions, monads in bicategories, 2-monads, biequivalences, the Bicategorical Yoneda Lemma, and the Coherence Theorem for bicategories. Grothendieck fibrations and the Grothendieck construction are discussed next, followed by tricategories, monoidal bicategories, the Gray tensor product, and double categories. Completely detailed proofs of several fundamental but hard-to-find results are presented for the first time. With exercises and plenty of motivation and explanation, this book is useful for both beginners and experts.

Recent Trends in Algebraic Development Techniques

José Luiz Fiadeiro,Ionuț Țuțu
Recent Trends in Algebraic Development Techniques Book PDF

Author : José Luiz Fiadeiro,Ionuț Țuțu
Publisher : Springer
Page : 175 pages
File Size : 52,5 Mb
Release : 2019-06-25
Category : Computers
ISBN : 9783030232207

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Recent Trends in Algebraic Development Techniques by José Luiz Fiadeiro,Ionuț Țuțu Pdf

This book constitutes the thoroughly refereed post-conference proceedings of the 24th IFIP WG 1.3 International Workshop on Algebraic Development Techniques, WADT 2018, held in Egham, UK in July 2018. The 9 revised papers presented were carefully reviewed and selected from 13 submissions. The contributed presentations covered a range of topics: specification and modelling languages such as CASL, Event-B, Maude, MMT, and SRML; foundations of system specification such as graph transformation, categorical semantics, fuzzy and temporal logics, institutions, module systems and parameterization, refinement, static analysis, and substitutions; and applications including categorical programming, communicating finite state machines, neuralsymbolicintegration, relational databases, and service-oriented computing.

Handbook of Algebra

M. Hazewinkel
Handbook of Algebra Book PDF

Author : M. Hazewinkel
Publisher : Elsevier
Page : 592 pages
File Size : 48,6 Mb
Release : 2009-07-08
Category : Mathematics
ISBN : 0080932819

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Handbook of Algebra by M. Hazewinkel Pdf

Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it is worthwhile to pursue the quest. In addition to the primary information given in the Handbook, there are references to relevant articles, books or lecture notes to help the reader. An excellent index has been included which is extensive and not limited to definitions, theorems etc. The Handbook of Algebra will publish articles as they are received and thus the reader will find in this third volume articles from twelve different sections. The advantages of this scheme are two-fold: accepted articles will be published quickly and the outline of the Handbook can be allowed to evolve as the various volumes are published. A particularly important function of the Handbook is to provide professional mathematicians working in an area other than their own with sufficient information on the topic in question if and when it is needed. - Thorough and practical source of information - Provides in-depth coverage of new topics in algebra - Includes references to relevant articles, books and lecture notes

The Local Structure of Algebraic K-Theory

Bjørn Ian Dundas,Thomas G. Goodwillie,Randy McCarthy
The Local Structure of Algebraic K Theory Book PDF

Author : Bjørn Ian Dundas,Thomas G. Goodwillie,Randy McCarthy
Publisher : Springer Science & Business Media
Page : 447 pages
File Size : 44,7 Mb
Release : 2012-09-06
Category : Mathematics
ISBN : 9781447143932

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The Local Structure of Algebraic K-Theory by Bjørn Ian Dundas,Thomas G. Goodwillie,Randy McCarthy Pdf

Algebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory and algebraic geometry. As is commonly encountered, this powerful mathematical object is very hard to calculate. Apart from Quillen's calculations of finite fields and Suslin's calculation of algebraically closed fields, few complete calculations were available before the discovery of homological invariants offered by motivic cohomology and topological cyclic homology. This book covers the connection between algebraic K-theory and Bökstedt, Hsiang and Madsen's topological cyclic homology and proves that the difference between the theories are ‘locally constant’. The usefulness of this theorem stems from being more accessible for calculations than K-theory, and hence a single calculation of K-theory can be used with homological calculations to obtain a host of ‘nearby’ calculations in K-theory. For instance, Quillen's calculation of the K-theory of finite fields gives rise to Hesselholt and Madsen's calculations for local fields, and Voevodsky's calculations for the integers give insight into the diffeomorphisms of manifolds. In addition to the proof of the full integral version of the local correspondence between K-theory and topological cyclic homology, the book provides an introduction to the necessary background in algebraic K-theory and highly structured homotopy theory; collecting all necessary tools into one common framework. It relies on simplicial techniques, and contains an appendix summarizing the methods widely used in the field. The book is intended for graduate students and scientists interested in algebraic K-theory, and presupposes a basic knowledge of algebraic topology.