In this paper we propose an approach to homotopical algebra where the basic ingredient is a category with two classes of distinguished morphisms: strong and weak equivalences. These data determine the cofibrant objects ...

We develop splitting techniques to study the Lyubeznik numbers of cover ideals of graphs which allow us to describe them for large families of graphs including forests, cycles, wheels and cactus graphs. More generally, we ...

Homotopy Theory focuses in the study of algebraic structures up to homotopy, a notion that allows to study algebraic invariants of topological and geometric origin. A classical technique in Homotopy Theory, introduced by ...