Derived invariance of Hochschild–Mitchell (co)homology and one-point extensions

In 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 long exact sequence à la Happel and we give a generalization of this result which provides an alternative approach.