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From categories to homotopy theory

Richter, Birgit, (1971-)

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From categories to homotopy theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	From categories to homotopy theory/ Birgit Richter.
Author:	Richter, Birgit,
Published:	Cambridge :Cambridge University Press, : 2020.,
Description:	x, 390 p. :ill., digital ;24 cm.
Notes:	Title from publisher's bibliographic system (viewed on 06 Apr 2020).
[NT 15003449]:	Basic notions in category theory -- Natural transformations and the Yoneda-Lemma -- (Co)limits -- Kan extensions -- Comma categories and the Grothendieck construction -- Monads and comonads -- Abelian categories -- Symmetric monoidal categories -- Enriched categories -- Simplicial objects -- The nerve and the classifying space of a small category -- A brief introduction to operads -- Classifying spaces of symmetric monoidal categories -- Approaches to iterated loop spaces via diagram categories -- Functor homology -- Homology and cohomology of small categories.
Subject:	Categories (Mathematics) -
Online resource:	https://doi.org/10.1017/9781108855891
ISBN:	9781108855891

From categories to homotopy theory
Richter, Birgit,1971-

From categories to homotopy theory[electronic resource] /Birgit Richter. - Cambridge :Cambridge University Press,2020. - x, 390 p. :ill., digital ;24 cm. - Cambridge studies in advanced mathematics ;188. - Cambridge studies in advanced mathematics ;188..

Title from publisher's bibliographic system (viewed on 06 Apr 2020).

Basic notions in category theory -- Natural transformations and the Yoneda-Lemma -- (Co)limits -- Kan extensions -- Comma categories and the Grothendieck construction -- Monads and comonads -- Abelian categories -- Symmetric monoidal categories -- Enriched categories -- Simplicial objects -- The nerve and the classifying space of a small category -- A brief introduction to operads -- Classifying spaces of symmetric monoidal categories -- Approaches to iterated loop spaces via diagram categories -- Functor homology -- Homology and cohomology of small categories.

Category theory provides structure for the mathematical world and is seen everywhere in modern mathematics. With this book, the author bridges the gap between pure category theory and its numerous applications in homotopy theory, providing the necessary background information to make the subject accessible to graduate students or researchers with a background in algebraic topology and algebra. The reader is first introduced to category theory, starting with basic definitions and concepts before progressing to more advanced themes. Concrete examples and exercises illustrate the topics, ranging from colimits to constructions such as the Day convolution product. Part II covers important applications of category theory, giving a thorough introduction to simplicial objects including an account of quasi-categories and Segal sets. Diagram categories play a central role throughout the book, giving rise to models of iterated loop spaces, and feature prominently in functor homology and homology of small categories.

ISBN: 9781108855891Subjects--Topical Terms:

525955
Categories (Mathematics)

LC Class. No.: QA169 / .R53 2020

Dewey Class. No.: 514.24

From categories to homotopy theory
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490 1 $a Cambridge studies in advanced mathematics ; $v 188
500 $a Title from publisher's bibliographic system (viewed on 06 Apr 2020).
505 0 $a Basic notions in category theory -- Natural transformations and the Yoneda-Lemma -- (Co)limits -- Kan extensions -- Comma categories and the Grothendieck construction -- Monads and comonads -- Abelian categories -- Symmetric monoidal categories -- Enriched categories -- Simplicial objects -- The nerve and the classifying space of a small category -- A brief introduction to operads -- Classifying spaces of symmetric monoidal categories -- Approaches to iterated loop spaces via diagram categories -- Functor homology -- Homology and cohomology of small categories.
520 $a Category theory provides structure for the mathematical world and is seen everywhere in modern mathematics. With this book, the author bridges the gap between pure category theory and its numerous applications in homotopy theory, providing the necessary background information to make the subject accessible to graduate students or researchers with a background in algebraic topology and algebra. The reader is first introduced to category theory, starting with basic definitions and concepts before progressing to more advanced themes. Concrete examples and exercises illustrate the topics, ranging from colimits to constructions such as the Day convolution product. Part II covers important applications of category theory, giving a thorough introduction to simplicial objects including an account of quasi-categories and Segal sets. Diagram categories play a central role throughout the book, giving rise to models of iterated loop spaces, and feature prominently in functor homology and homology of small categories.
650 0 $a Categories (Mathematics) $3 525955
650 0 $a Homotopy theory. $3 604501
830 0 $a Cambridge studies in advanced mathematics ; $v 188. $3 3469106
856 4 0 $u https://doi.org/10.1017/9781108855891