Baues-Wirsching Cohomology and Svarc Genus in Small Categories
Category Theory
2026-05-19 v2 Algebraic Topology
Abstract
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 in any natural system is a lower bound for the homotopic sectional category (also called Svarc genus). Our results extend classical Svarc type inequalties to the categorical setting and introduce a computationally efficient method via a reduced cochain complex for Baues-Wirching cohomology.
Cite
@article{arxiv.2508.00727,
title = {Baues-Wirsching Cohomology and Svarc Genus in Small Categories},
author = {Isaac Carcacía-Campos and Enrique Macías-Virgós and David Mosquera-Lois},
journal= {arXiv preprint arXiv:2508.00727},
year = {2026}
}