Descent in ∗ -autonomous categories

We extend the result of Joyal and Tierney asserting that a morphism of commutative algebras in the ∗-autonomous category of sup-lattices is an effective descent morphism for modules if and only if it is pure, to an arbitrary ∗-autonomous category VV (in which the tensor unit is projective) by showing that any VV-functor out of VV is precomonadic if and only if it is comonadic.