Baues-Wirsching cohomology and Svarc genus in small categories

Abstract

We prove that for a bifibration P between small categories, the length of the cup product in the kernel of the induced morphism P^* in the Baues-Wirsching cohomology with coefficients in any natural system is a lower bound for the homotopic sectional category (also called Svarc genus) of P. Our results extend classical Svarc-type inequalities to the categorical setting and introduce a computationally efficient method via a reduced cochain complex for Baues–Wirsching cohomology.