Introduction to Abstract Homotopy Theory

Abstract

This is an introduction to the study of abstract homotopy theory by means of model categories and $(\infty ,1)$-categories. The only prerequisites are very basic general topology and abstract algebra. None categorical background is needed. The final objective is to show that classical homotopy theory for topological spaces can be more naturally understood in terms of categorical language.

arXiv commentIn Brazilian portuguese. Preliminary version of the namesake book published by NEA

References in corpus (6)

• Higher Topos Theory
• Higher Operads, Higher Categories
• A short course on $\infty$-categories
• Weak complicial sets, a simplicial weak omega-category theory. Part I: basic homotopy theory
• Weak complicial sets, a simplicial weak omega-category theory. Part II: nerves of complicial Gray-categories
• Complicial structures in the nerves of omega-categories