Quasi-cotripleable categories
Robert Davis · Proceedings of the American Mathematical Society · 1972
A category is quasi-cotripleable over the category of sets if it has all the properties of cotripleable categories except the right adjoint to the forgetful functor. Problems involving such categories are illustrated by categories of relational structures, and by categories of sets acted on by a monoid with open homomorphisms for maps. A characterization is given in terms of generalized operators and relations.