Una introducción a las categorías extrianguladas

English translation of the abstract: Currently, the basic structures used in the study of homological algebra are abelian categories, exact categories and triangulated categories. A particular relationship between exact and triangulated categories is well-known–given by Frobenius categories and their associated stable categories–, and many results of homological nature are valid in both contexts. However, the processes for transfering results between these two types of categories are quite complex. In order to overcome these difficulties, in 2019 H. Nakaoka and Y. Palu introduced a simultaneous generalization of exact categories and triangulated categories, axiomatizing the properties of the Ext¹ bifunctors in both contexts which are relevant for the definition of cotorsion pairs, which they called extriangulated category. In this talk, we will give an introduction to this recently defined type of category and discuss some of its fundamental results. Links: abstract (in Spanish).