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Introdução às infinito-categorias
(Universidade Federal de São Carlos, 2025-04-26) Miguel, Marina Maria de; Ruffino, Fabio Ferrari; https://lattes.cnpq.br/2512107188781159; https://orcid.org/0000-0002-8607-3715; https://lattes.cnpq.br/5724402579792207; https://orcid.org/0000-0003-1121-1041
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.