Homotopía de categorías y carcajes finitos y su relación con la cohomología de Hochschild de las álgebras de caminos

Abstract

In this paper we present a homotopy theory for the study of the first fundamental group of a finite category. Later, given a bound quiver we construct a category and study the relation between the first fundamental groups of this category and the bound quiver, contrasting both results with the first fundamental group of the classifying space of the bound quiver. Finally we study if there exists a relation between the first homotopy group of a quiver and the first Hochschild cohomology group of its path algebra.