7 papers
Weak and Strong Fibrations of Functors
Isaac Carcacía-Campos, Enrique Macías-Virgós, David Mosquera-Lois
We develop a homotopical framework for small categories that extends classical invarints of algebraic topology to the categorical setting. Our approach is based on the construction…
A Computational (Co)homological Approach to Contiguity Distance
Enrique Macías-Virgós, Ángel Méndez-Vázquez, David Mosquera-Lois
We introduce two new algebraic invariants, the (co)homological distances between continuous maps, which provide computable lower bounds for the homotopic distance and strictly refi…
Baues-Wirsching Cohomology and Svarc Genus in Small Categories
Isaac Carcacía-Campos, Enrique Macías-Virgós, David Mosquera-Lois
We prove that for a bifibration P between small categories, the lenght of the cup product in the kernel of the induced morphism in the Baues-Wirsching cohomology with coefficients…
Lefschetz fixed-object and fixed-morphism theorems for acyclic categories
Samuel Castelo-Mourelle, Enrique Macías-Virgós, David Mosquera-Lois
We introduce two novel complementary notions of the Lefschetz number for a functor from a finite acyclic category to itself and we prove a Lefschetz fixed-object theorem and a Lefs…
Homotopy invariants in small categories
I. Carcacía-Campos, E. Macías-Virgós, D. Mosquera-Lois
Tanaka introduced a notion of Lusternik Schnirelmann category, denoted , of a small category . Among other properties, he proved an analog…
Morse theory for loop-free categories
Michał Lipiński, David Mosquera-Lois, Mateusz Przybylski
We extend discrete Morse-Bott theory to the setting of loop-free (or acyclic) categories. First of all, we state a homological version of Quillen's Theorem A in this context and in…
Euler calculus on spaces homeomorphic to definable sets and some applications
E. Macías-Virgós, D. Mosquera-Lois
We show that integration with respect to the Euler-Poincaré characteristic can be extended from the setting of definable sets to the setting of topological spaces homeomorphic to d…