A new perspective on comodules of polynomial comonads
Bryce Clarke
Tallinn University of Technology
Abstract:
Categories, functors, profunctors, and natural transformations
form the building blocks of category theory. Recently in the
seminar, Priyaa spoke about viewing categories as polynomial
comonads, however the notion of comonad morphism and comodule we
obtain are quite different to functors and profunctors. Morphisms
of polynomial comonads are spans of an identity-on-objects
functor and a discrete opfibration, while comodules of polynomial
comonads are spans of a profunctor and a discrete opfibration. In
this talk, I will explain these notions, provide examples, and
demonstrate a new characterisation of comodules of polynomial
comonads as functors A^{op} x B -> Poly.