Introdução às infinito-categorias

Abstract

There are several ways to define infinity-categories; although they all have the same essence, some of them are more difficult to handle. Here we define the notion of infinity-category through the language of simplicial sets, which is easier to work with. As a preliminary step, we make a brief introduction to category theory and we discuss some relevant tools and results in this framework (categorical (co)limits, Yoneda's lemma, Kan's extension, nerve of a category). Moreover, we introduce the notion of 2-Category and we use it to guess the structure of n-categories and infinity-categories.