From categories to homotopy theory
From categories to homotopy theory:

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 acc...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
1. Verfasser: Richter, Birgit 1971- (VerfasserIn)
Format: Elektronisch E-Book
Sprache:English
Veröffentlicht: Cambridge Cambridge University Press 2020
Schriftenreihe:Cambridge studies in advanced mathematics
188
Schlagworte:
Categories (Mathematics)
Homotopy theory
Kategorie > Mathematik
Homotopietheorie
Online-Zugang:DE-12
DE-92
DE-384
DE-29
URL des Erstveröffentlichers
Zusammenfassung: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
Beschreibung: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
Beschreibung:1 Online-Ressource (x, 390 Seiten)
ISBN:9781108855891
DOI:10.1017/9781108855891

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