Gm. Kelly et Aj. Power, ADJUNCTIONS WHOSE COUNITS ARE COEQUALIZERS, AND PRESENTATIONS OF FINITARY ENRICHED MONADS, Journal of pure and applied algebra, 89(1-2), 1993, pp. 163-179
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 appl
y this to show that every finitary monad on a locally-finitely-present
able enriched category A admits a presentation in terms of basic opera
tions and equations between derived operations, the arties here being
the finitely-presentable objects of A.