Finite-product-preserving functors, Kan extensions, and strongly-finitary 2-monads (Q690382)

The authors study the 2-monads on the 2-category CAT of small categories, which are completely determined, in the following sense, by their action on the finite discrete categories: the monad \(T\) is the left Kan extension of its restriction to the finite discrete categories. The authors investigate in particular the relations between this problem and the preservation of finite products by a left Kan extension.