Higher Topos Theory Am 170
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Higher Topos Theory
Author | : Jacob Lurie |
Publsiher | : Princeton University Press |
Total Pages | : 944 |
Release | : 2009-07-26 |
Genre | : Mathematics |
ISBN | : 9780691140483 |
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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.
Higher Topos Theory AM 170
Author | : Jacob Lurie |
Publsiher | : Princeton University Press |
Total Pages | : 944 |
Release | : 2009-07-06 |
Genre | : Mathematics |
ISBN | : 9781400830558 |
Download Higher Topos Theory AM 170 Book in PDF, Epub and Kindle
Higher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinity-categories, higher categories in which all higher morphisms are assumed to be invertible. 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. The result is a powerful theory with applications in many areas of mathematics. The book's first five chapters give an exposition of the theory of infinity-categories that emphasizes their role as a generalization of ordinary categories. Many of the fundamental ideas from classical category theory are generalized to the infinity-categorical setting, such as limits and colimits, adjoint functors, ind-objects and pro-objects, locally accessible and presentable categories, Grothendieck fibrations, presheaves, and Yoneda's lemma. A sixth chapter presents an infinity-categorical version of the theory of Grothendieck topoi, introducing the notion of an infinity-topos, an infinity-category that resembles the infinity-category of topological spaces in the sense that it satisfies certain axioms that codify some of the basic principles of algebraic topology. A seventh and final chapter presents applications that illustrate connections between the theory of higher topoi and ideas from classical topology.
Lectures on Factorization Homology Categories and Topological Field Theories
Author | : Hiro Lee Tanaka |
Publsiher | : Springer Nature |
Total Pages | : 84 |
Release | : 2020-12-14 |
Genre | : Science |
ISBN | : 9783030611637 |
Download Lectures on Factorization Homology Categories and Topological Field Theories Book in PDF, Epub and Kindle
This book provides an informal and geodesic introduction to factorization homology, focusing on providing intuition through simple examples. Along the way, the reader is also introduced to modern ideas in homotopy theory and category theory, particularly as it relates to the use of infinity-categories. As with the original lectures, the text is meant to be a leisurely read suitable for advanced graduate students and interested researchers in topology and adjacent fields.
Category Theory in Context
Author | : Emily Riehl |
Publsiher | : Courier Dover Publications |
Total Pages | : 272 |
Release | : 2017-03-09 |
Genre | : Mathematics |
ISBN | : 9780486820804 |
Download Category Theory in Context Book in PDF, Epub and Kindle
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.
Basic Category Theory
Author | : Tom Leinster |
Publsiher | : Cambridge University Press |
Total Pages | : 193 |
Release | : 2014-07-24 |
Genre | : Mathematics |
ISBN | : 9781107044241 |
Download Basic Category Theory Book in PDF, Epub and Kindle
A short introduction ideal for students learning category theory for the first time.
Elements of Category Theory
Author | : Emily Riehl,Dominic Verity |
Publsiher | : Cambridge University Press |
Total Pages | : 781 |
Release | : 2022-02-10 |
Genre | : Mathematics |
ISBN | : 9781108837989 |
Download Elements of Category Theory Book in PDF, Epub and Kindle
This book develops the theory of infinite-dimensional categories by studying the universe, or ∞-cosmos, in which they live.
From Categories to Homotopy Theory
Author | : Birgit Richter |
Publsiher | : Cambridge University Press |
Total Pages | : 401 |
Release | : 2020-04-16 |
Genre | : Mathematics |
ISBN | : 9781108479622 |
Download From Categories to Homotopy Theory Book in PDF, Epub and Kindle
Bridge the gap between category theory and its applications in homotopy theory with this guide for graduate students and researchers.
An Introduction to Category Theory
Author | : Harold Simmons |
Publsiher | : Cambridge University Press |
Total Pages | : 135 |
Release | : 2011-09-22 |
Genre | : Mathematics |
ISBN | : 9781139503327 |
Download An Introduction to Category Theory Book in PDF, Epub and Kindle
Category theory provides a general conceptual framework that has proved fruitful in subjects as diverse as geometry, topology, theoretical computer science and foundational mathematics. Here is a friendly, easy-to-read textbook that explains the fundamentals at a level suitable for newcomers to the subject. Beginning postgraduate mathematicians will find this book an excellent introduction to all of the basics of category theory. It gives the basic definitions; goes through the various associated gadgetry, such as functors, natural transformations, limits and colimits; and then explains adjunctions. The material is slowly developed using many examples and illustrations to illuminate the concepts explained. Over 200 exercises, with solutions available online, help the reader to access the subject and make the book ideal for self-study. It can also be used as a recommended text for a taught introductory course.