Flows With Respect to a Functor

Flows with respect to a functor F are introduced as a common generalization of the concepts of F-co-structured sinks and small F-co-structured sources. Appropriate factorization structures for functors are investigated and used to obtain several results that characterize coadjoint functors that have domains with various completeness conditions. When the functor in question is an identity functor, these results reduce to earlier results of Herrlich and Meyer for flows in a category. Functors of the type in question are shown to be nicely behaved with respect to composition. The dual notion of wolfs with respect to a functor is introduced, as is the concept of (co)limit with respect to a functor.