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Higher Topos Theory
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Book Synopsis Higher Topos Theory by : Jacob Lurie
Download or read book Higher Topos Theory written by Jacob Lurie and published by Princeton University Press. This book was released on 2009-07-26 with total page 944 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 'Higher Topos Theory', Jacob Lurie presents the foundations of this theory using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language.
Book Synopsis Higher Topos Theory (AM-170) by : Jacob Lurie
Download or read book Higher Topos Theory (AM-170) written by Jacob Lurie and published by Princeton University Press. This book was released on 2009-07-26 with total page 948 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 'Higher Topos Theory', Jacob Lurie presents the foundations of this theory using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language.
Book Synopsis Higher Categories and Homotopical Algebra by : Denis-Charles Cisinski
Download or read book Higher Categories and Homotopical Algebra written by Denis-Charles Cisinski and published by Cambridge University Press. This book was released on 2019-05-02 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: At last, a friendly introduction to modern homotopy theory after Joyal and Lurie, reaching advanced tools and starting from scratch.
Book Synopsis Higher Category Theory by : Ezra Getzler
Download or read book Higher Category Theory written by Ezra Getzler and published by American Mathematical Soc.. This book was released on 1998 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprises six presentations on new developments in category theory from the March 1997 workshop. The topics are categorification, computads for finitary monads on globular sets, braided n- categories and a-structures, categories of vector bundles and Yang- Mills equations, the role of Michael Batanin's monoidal globular categories, and braided deformations of monoidal categories and Vassiliev invariants. No index. Annotation copyrighted by Book News, Inc., Portland, OR.
Book Synopsis Categories for the Working Mathematician by : Saunders Mac Lane
Download or read book Categories for the Working Mathematician written by Saunders Mac Lane and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Elements of ∞-Category Theory by : Emily Riehl
Download or read book Elements of ∞-Category Theory written by Emily Riehl and published by Cambridge University Press. This book was released on 2022-02-10 with total page 782 pages. Available in PDF, EPUB and Kindle. Book excerpt: The language of ∞-categories provides an insightful new way of expressing many results in higher-dimensional mathematics but can be challenging for the uninitiated. To explain what exactly an ∞-category is requires various technical models, raising the question of how they might be compared. To overcome this, a model-independent approach is desired, so that theorems proven with any model would apply to them all. This text develops the theory of ∞-categories from first principles in a model-independent fashion using the axiomatic framework of an ∞-cosmos, the universe in which ∞-categories live as objects. An ∞-cosmos is a fertile setting for the formal category theory of ∞-categories, and in this way the foundational proofs in ∞-category theory closely resemble the classical foundations of ordinary category theory. Equipped with exercises and appendices with background material, this first introduction is meant for students and researchers who have a strong foundation in classical 1-category theory.
Book Synopsis Categorical Homotopy Theory by : Emily Riehl
Download or read book Categorical Homotopy Theory written by Emily Riehl and published by Cambridge University Press. This book was released on 2014-05-26 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admit a compatible model structure, or through particular formulae that give the right notion in certain examples. Emily Riehl unifies these seemingly rival perspectives and demonstrates that model structures on diagram categories are irrelevant. Homotopy (co)limits are explained to be a special case of weighted (co)limits, a foundational topic in enriched category theory. In Part II, Riehl further examines this topic, separating categorical arguments from homotopical ones. Part III treats the most ubiquitous axiomatic framework for homotopy theory - Quillen's model categories. Here, Riehl simplifies familiar model categorical lemmas and definitions by focusing on weak factorization systems. Part IV introduces quasi-categories and homotopy coherence.
Book Synopsis Basic Category Theory by : Tom Leinster
Download or read book Basic Category Theory written by Tom Leinster and published by Cambridge University Press. This book was released on 2014-07-24 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: A short introduction ideal for students learning category theory for the first time.
Book Synopsis Sketches of an Elephant: A Topos Theory Compendium by : P. T. Johnstone
Download or read book Sketches of an Elephant: A Topos Theory Compendium written by P. T. Johnstone and published by Oxford University Press. This book was released on 2002-09-12 with total page 836 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topos Theory is a subject that stands at the junction of geometry, mathematical logic and theoretical computer science, and it derives much of its power from the interplay of ideas drawn from these different areas. Because of this, an account of topos theory which approaches the subject from one particular direction can only hope to give a partial picture; the aim of this compendium is to present as comprehensive an account as possible of all the main approaches and to thereby demonstrate the overall unity of the subject. The material is organized in such a way that readers interested in following a particular line of approach may do so by starting at an appropriate point in the text.
Book Synopsis Category Theory in Context by : Emily Riehl
Download or read book Category Theory in Context written by Emily Riehl and published by Courier Dover Publications. This book was released on 2017-03-09 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.
Book Synopsis Higher Operads, Higher Categories by : Tom Leinster
Download or read book Higher Operads, Higher Categories written by Tom Leinster and published by Cambridge University Press. This book was released on 2004-07-22 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foundations of higher dimensional category theory for graduate students and researchers in mathematics and mathematical physics.
Book Synopsis Homotopy Type Theory: Univalent Foundations of Mathematics by :
Download or read book Homotopy Type Theory: Univalent Foundations of Mathematics written by and published by Univalent Foundations. This book was released on with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Higher-Order Categorical Logic by : J. Lambek
Download or read book Introduction to Higher-Order Categorical Logic written by J. Lambek and published by Cambridge University Press. This book was released on 1988-03-25 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part I indicates that typed-calculi are a formulation of higher-order logic, and cartesian closed categories are essentially the same. Part II demonstrates that another formulation of higher-order logic is closely related to topos theory.
Book Synopsis An Invitation to Applied Category Theory by : Brendan Fong
Download or read book An Invitation to Applied Category Theory written by Brendan Fong and published by Cambridge University Press. This book was released on 2019-07-18 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Category theory is unmatched in its ability to organize and layer abstractions and to find commonalities between structures of all sorts. No longer the exclusive preserve of pure mathematicians, it is now proving itself to be a powerful tool in science, informatics, and industry. By facilitating communication between communities and building rigorous bridges between disparate worlds, applied category theory has the potential to be a major organizing force. This book offers a self-contained tour of applied category theory. Each chapter follows a single thread motivated by a real-world application and discussed with category-theoretic tools. We see data migration as an adjoint functor, electrical circuits in terms of monoidal categories and operads, and collaborative design via enriched profunctors. All the relevant category theory, from simple to sophisticated, is introduced in an accessible way with many examples and exercises, making this an ideal guide even for those without experience of university-level mathematics.
Book Synopsis Towards Higher Categories by : John C. Baez
Download or read book Towards Higher Categories written by John C. Baez and published by Springer Science & Business Media. This book was released on 2009-09-24 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to give background for those who would like to delve into some higher category theory. It is not a primer on higher category theory itself. It begins with a paper by John Baez and Michael Shulman which explores informally, by analogy and direct connection, how cohomology and other tools of algebraic topology are seen through the eyes of n-category theory. The idea is to give some of the motivations behind this subject. There are then two survey articles, by Julie Bergner and Simona Paoli, about (infinity,1) categories and about the algebraic modelling of homotopy n-types. These are areas that are particularly well understood, and where a fully integrated theory exists. The main focus of the book is on the richness to be found in the theory of bicategories, which gives the essential starting point towards the understanding of higher categorical structures. An article by Stephen Lack gives a thorough, but informal, guide to this theory. A paper by Larry Breen on the theory of gerbes shows how such categorical structures appear in differential geometry. This book is dedicated to Max Kelly, the founder of the Australian school of category theory, and an historical paper by Ross Street describes its development.
Book Synopsis Sets for Mathematics by : F. William Lawvere
Download or read book Sets for Mathematics written by F. William Lawvere and published by Cambridge University Press. This book was released on 2003-01-27 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.
Book Synopsis Simplicial Homotopy Theory by : Paul G. Goerss
Download or read book Simplicial Homotopy Theory written by Paul G. Goerss and published by Birkhäuser. This book was released on 2012-12-06 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the beginning of the modern era of algebraic topology, simplicial methods have been used systematically and effectively for both computation and basic theory. With the development of Quillen's concept of a closed model category and, in particular, a simplicial model category, this collection of methods has become the primary way to describe non-abelian homological algebra and to address homotopy-theoretical issues in a variety of fields, including algebraic K-theory. This book supplies a modern exposition of these ideas, emphasizing model category theoretical techniques. Discussed here are the homotopy theory of simplicial sets, and other basic topics such as simplicial groups, Postnikov towers, and bisimplicial sets. The more advanced material includes homotopy limits and colimits, localization with respect to a map and with respect to a homology theory, cosimplicial spaces, and homotopy coherence. Interspersed throughout are many results and ideas well-known to experts, but uncollected in the literature. Intended for second-year graduate students and beyond, this book introduces many of the basic tools of modern homotopy theory. An extensive background in topology is not assumed.
