Introdução às categorias modelo

Abstract

This work presents an introduction to model category theory, a groundbreaking concept introduced by Daniel Quillen in the 1960s, which provides a unified framework for the study of homotopical structures across various areas of mathematics. We explore the model category structure in three fundamental contexts: the category of R-modules complexes, the category of topological spaces, and the category of simplicial categories. For each of these categories, we present the corresponding model structure, detail its essential properties, and discuss its applications. The aim of this work is to provide an introductory and accessible exposition of the subject, emphasizing the importance of model categories in unifying homotopical and algebraic concepts.