Re: Monads on finite categories

Hello, Tom Leinster wrote:

1. Are there significant or interesting examples of monads on finite categories? I want to look beyond monads on posets, a.k.a. closure operators. (Since a finite category with binary sums or products is necessarily a poset, some of the usual examples of monads reduce to this case.) I can only think of one class of examples (described below), and I don't know if it's particularly significant.

Idempotent monads correspond to full reflective subcategories; so the only examples are induced by full reflective subcategories of finite categories. Greetings Reinhard