4 papers
Morse theory for loop-free categories
MichaÅ LipiÅski, 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…
Weak and Strong Fibrations of Functors
Isaac CarcacÃa-Campos, Enrique MacÃas-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…
Baues-Wirsching Cohomology and Svarc Genus in Small Categories
Isaac CarcacÃa-Campos, Enrique MacÃas-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…
A Computational (Co)homological Approach to Contiguity Distance
Enrique MacÃas-Virgós, Ãngel 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…