Cambridge Studies in Advanced Mathematics: Series Number 180: Higher Categories and Homotopical Alge

Denis-Charles Cisinski

448 pages, parution le 29/04/2019

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Résumé

This user-friendly book introduces modern homotopy theory through the lens of higher categories after Joyal and Lurie. Starting from scratch it guides graduate students and researchers through the powerful tools that the theory provides for applications in such areas as algebraic geometry, representation theory, algebra and logic.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.Preface; 1. Prelude; 2. Basic homotopical algebra; 3. The homotopy theory of -categories; 4. Presheaves: externally; 5. Presheaves: internally; 6. Adjoints, limits and Kan extensions; 7. Homotopical algebra; References; Notation; Index.Denis-Charles Cisinski is Professor of Mathematics at the Universitat Regensburg, Germany. His research focuses on homotopical algebra, category theory, K-theory and the cohomology of schemes. He is also the author of a monograph entitled Les prefaisceaux comme modeles des types d'homotopie (2007).

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Denis-Charles Cisinski
Parution	29/04/2019
Nb. de pages	448
EAN13	9781108473200

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Cambridge Studies in Advanced Mathematics: Series Number 180: Higher Categories and Homotopical Alge

Résumé

Caractéristiques techniques

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