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Higher categories and homotopical al...

Cisinski, Denis-Charles.

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Higher categories and homotopical algebra

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Higher categories and homotopical algebra/ Denis-Charles Cisinski.
作者:	Cisinski, Denis-Charles.
出版者:	Cambridge :Cambridge University Press, : 2019.,
面頁冊數:	xviii, 430 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 24 Apr 2019).
內容註:	Prelude -- Basic homotopical algebra -- The homotopy theory of 8-categories -- Presheaves : externally -- Presheaves : internally -- Adjoints, limits and kan extensions -- Homotopical algebra.
標題:	Homotopy theory. -
電子資源:	https://doi.org/10.1017/9781108588737
ISBN:	9781108588737

Higher categories and homotopical algebra
Cisinski, Denis-Charles.

Higher categories and homotopical algebra[electronic resource] /Denis-Charles Cisinski. - Cambridge :Cambridge University Press,2019. - xviii, 430 p. :ill., digital ;24 cm. - Cambridge studies in advanced mathematics ;180. - Cambridge studies in advanced mathematics ;180..

Title from publisher's bibliographic system (viewed on 24 Apr 2019).

Prelude -- Basic homotopical algebra -- The homotopy theory of 8-categories -- Presheaves : externally -- Presheaves : internally -- Adjoints, limits and kan extensions -- Homotopical algebra.

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.

ISBN: 9781108588737Subjects--Topical Terms:

604501
Homotopy theory.

LC Class. No.: QA612.7 / .C5645 2019

Dewey Class. No.: 514.24

Higher categories and homotopical algebra
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490 1 $a Cambridge studies in advanced mathematics ; $v 180
500 $a Title from publisher's bibliographic system (viewed on 24 Apr 2019).
505 0 $a Prelude -- Basic homotopical algebra -- The homotopy theory of 8-categories -- Presheaves : externally -- Presheaves : internally -- Adjoints, limits and kan extensions -- Homotopical algebra.
520 $a 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.
650 0 $a Homotopy theory. $3 604501
650 0 $a Algebra, Homological. $3 663850
650 0 $a Categories (Mathematics) $3 525955
650 0 $a Presheaves. $3 3470598
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