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

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