Introduction to Infinity-Categories

✍ Scribed by Markus Land

• Publisher: Springer Nature
• Tongue: English
• Leaves: 300
• Category: Library

✦ Table of Contents

Preface
Acknowledgments
Contents
1 Categories, Simplicial Sets, and Infinity-Categories
Motivation and Overview
1.1 Categories and Simplicial Sets
1.2 ∞-Categories
1.3 Anodyne Maps and Fibrations
1.4 Joins and Slices
2 Joyal's Theorem, Applications, and Dwyer–Kan Localizations
2.1 Joyal's Special Horn Lifting Theorem
2.2 Pointwise Criterion for Natural Equivalences
2.3 Fully Faithful and Essentially Surjective Functors
2.4 Localizations
2.5 Fat Joins, Fat Slices and Mapping Spaces
3 (Co)Cartesian Fibrations and the Construction of Functors
3.1 (Co)Cartesian Fibrations
3.2 Marked Simplicial Sets and Marked Anodyne Maps
3.3 Straightening-Unstraightening
4 Limits, Colimits, and Quillen's Theorem A
4.1 Terminal and Initial Objects
4.2 The Yoneda Lemma for ∞-Categories
4.3 Limits and Colimits
4.4 Cofinal and Coinitial Functors
5 Adjunctions and Adjoint Functor Theorems
5.1 Adjunctions
5.2 Adjoint Functor Theorems
A Exercises
Bibliography