Galois coverings, Morita equivalence and smash extensions of categories   over a field
  We consider categories over a field $k$ in order to prove that smash extensions and Galois coverings with respect to a finite group coincide up to Morita equivalence of $k$-categories. For this purpose we describe processes providing Morita equivalences called contraction and expansion. We prove that composition of these processes provides any Morita equivalence, a result which is related with the karoubianisation (or idempotent completion) and additivisation of a $k$-category. 
Claude Cibils (Institut de Math\'ematiques et de Mod\'elisation de   Montpellier), Andrea Solotar