Higher categories and homotopical algebra

✍ Scribed by Denis-Charles Cisinski

Publisher: Cambridge University Press
Year: 2019
Tongue: English
Leaves: 449
Series: Cambridge studies in advanced mathematics 180
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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.

✦ Table of Contents

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

✦ Subjects

Homotopy theory;Algebra, Homological;Categories (Mathematics);Presheaves

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