2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165831Let C be a small category and k a field. There are two interesting mathematical subjects: the category algebra kC and the classifying space |C|=BC. We study the ring homomorphism HH*(kC) --> H*(|C|,k) and prove it is split surjective. This generalizes the well-known results for groups and posets. Based on this result, we construct a seven-dimensional category algebra whose Hochschild cohomology ring modulo nilpotents is not finitely generated, against a conjecture of Snashall and Solberg.Advances in Mathematics, to appearAlgebraic TopologyRings and Algebras18A25, 18A40, 16E30, 16E40text