2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115464In this article we prove derived invariance of Hochschild-Mitchell homology and cohomology and we extend to $k$-linear categories a result by Barot and Lenzing concerning derived equivalences and one-point extensions. We also prove the existence of a Happel long exact sequence and we give a generalization of this result which provides an alternative approach.17 pagesK-Theory and HomologyRings and Algebras16E40, 18E05, 18E30, 16E40, 18E05, 18E30, 16D90text