Trivial Extensions of Abelian Categories, Recollement and Applications

Abstract

In this paper,we first study conditions under which a recollement relative to abelian categories induces a new recollement relative to trivial extensions of abelian categories.Applying our results to module categories of rings,we prove that trivial extensions of Morita equivalent rings by the corresponding bimodules are Morita equivalent,especially for one-point extension rings.For the idempotent completion of additive categories,we get a recollement about trivial extensions of idempotent completion categories.