Descent in Locally Presentable Categories

Let (mathbb {V}=(VV, otimes , I)) be a symmetric monoidal category such that (mathcal {V}) is locally presentable and that all functors (Votimes - : mathcal {V} rightarrow mathcal {V}) for (V in mathcal {V}) preserve reflexive coequalizers and directed colimits. It is proved that any pure morphism of commutative ??-monoids is an effective descent morphism with respect to the indexed category given by commutative ??-monoids and modules over them. As a by-product, we prove that pure morphisms in a locally presentable category are effective for codescent.