ADJUNCTIONS WHOSE COUNITS ARE COEQUALIZERS, AND PRESENTATIONS OF FINITARY ENRICHED MONADS

A right adjoint functor is said to be of descent type if the counit of the adjunction is pointwise a coequalizer. Building on the results of Tholen's doctoral thesis, we give necessary and sufficient conditions for a composite to be of descent type when each factor is so. We apply this to show that every finitary monad on a locally-finitely-presentable enriched category A admits a presentation in terms of basic operations and equations between derived operations, the arties here being the finitely-presentable objects of A.