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.
Revised on April 13, 2016 13:09:48
by Mike Shulman