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Higher Categories and Homotopical Algebra

2019-05-02 Mathematics
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Release : 2019-05-02
Genre : Mathematics
Kind : eBook
Book Rating : 202/5 ( reviews)

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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. This book was released on 2019-05-02. 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.

Higher Categories and Homotopical Algebra

2019-05-02 Mathematics
Download Higher Categories and Homotopical Algebra PDF Online Free

Author :
Release : 2019-05-02
Genre : Mathematics
Kind : eBook
Book Rating : 477/5 ( reviews)

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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. This book was released on 2019-05-02. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to modern homotopy theory through the lens of higher categories after Joyal and Lurie, giving access to methods used at the forefront of research in algebraic topology and algebraic geometry in the twenty-first century. The text starts from scratch - revisiting results from classical homotopy theory such as Serre's long exact sequence, Quillen's theorems A and B, Grothendieck's smooth/proper base change formulas, and the construction of the Kan–Quillen model structure on simplicial sets - and develops an alternative to a significant part of Lurie's definitive reference Higher Topos Theory, with new constructions and proofs, in particular, the Yoneda Lemma and Kan extensions. The strong emphasis on homotopical algebra provides clear insights into classical constructions such as calculus of fractions, homotopy limits and derived functors. For graduate students and researchers from neighbouring fields, this book is a user-friendly guide to advanced tools that the theory provides for application.

Homotopy Theory of Higher Categories

2011-10-20 Mathematics
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Release : 2011-10-20
Genre : Mathematics
Kind : eBook
Book Rating : 190/5 ( reviews)

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Book Synopsis Homotopy Theory of Higher Categories by : Carlos Simpson

Download or read book Homotopy Theory of Higher Categories written by Carlos Simpson. This book was released on 2011-10-20. Available in PDF, EPUB and Kindle. Book excerpt: The study of higher categories is attracting growing interest for its many applications in topology, algebraic geometry, mathematical physics and category theory. In this highly readable book, Carlos Simpson develops a full set of homotopical algebra techniques and proposes a working theory of higher categories. Starting with a cohesive overview of the many different approaches currently used by researchers, the author proceeds with a detailed exposition of one of the most widely used techniques: the construction of a Cartesian Quillen model structure for higher categories. The fully iterative construction applies to enrichment over any Cartesian model category, and yields model categories for weakly associative n-categories and Segal n-categories. A corollary is the construction of higher functor categories which fit together to form the (n+1)-category of n-categories. The approach uses Tamsamani's definition based on Segal's ideas, iterated as in Pelissier's thesis using modern techniques due to Barwick, Bergner, Lurie and others.

Categorical Homotopy Theory

2014-05-26 Mathematics
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Release : 2014-05-26
Genre : Mathematics
Kind : eBook
Book Rating : 633/5 ( reviews)

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Book Synopsis Categorical Homotopy Theory by : Emily Riehl

Download or read book Categorical Homotopy Theory written by Emily Riehl. This book was released on 2014-05-26. 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.

Homotopy Type Theory: Univalent Foundations of Mathematics

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Book Synopsis Homotopy Type Theory: Univalent Foundations of Mathematics by :

Download or read book Homotopy Type Theory: Univalent Foundations of Mathematics written by . This book was released on . Available in PDF, EPUB and Kindle. Book excerpt:

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