Differential torsion theories on Eilenberg-Moore categories of monads

Abstract

Let $C$ be a Grothendieck category and U be a monad on $C$ that is exact and preserves colimits. In this article, we prove that every hereditary torsion theory on the Eilenberg-Moore category of modules over a monad U is differential. Furthermore, if $\delta :U⟶U$ denotes a derivation on a monad U, then we show that every δ-derivation on a U-module M extends uniquely to a δ-derivation on the module of quotients of M.