A functor is pseudomonic if
More generally, a morphism in any 2-category is called pseudomonic morphism if the square analogous to that below is a pullback, or equivalently if is a pseudomonic functor for any .
Every full and faithful functor is pseudomonic, and every pseudomonic functor is conservative. A functor is pseudomonic if and only if the square
An interesting example of the notion appears in the context of Joyal’s species of structures.
A species is a functor from the category of finite sets and bijections to , and the functors that are obtained by taking left Kan extensions of species along the embedding are called analytic functors. Now taking left Kan extensions along is pseudomonic, and this implies that the coefficients of an analytic functor are unique up to isomorphism.
Arguably, pseudomonic functors are precisely the functors for which it makes sense to say that is uniquely determined by up to unique isomorphism. However, we do not really need faithfulness for this; bijectivity on isos suffices.
Last revised on June 3, 2019 at 07:18:44. See the history of this page for a list of all contributions to it.