Descent in Locally Presentable Categories

Let be a symmetric monoidal category such that is locally presentable and that all functors for preserve reflexive coequalizers and directed colimits. It is proved that any pure morphism of commutative oe center dot i-monoids is an effective descent morphism with respect to the indexed category given by commutative oe center dot i-monoids and modules over them. As a by-product, we prove that pure morphisms in a locally presentable category are effective for codescent.