Polynomials, fibrations and distributive laws

Tamara von Glehn

We study the structure of the category of polynomials in a locally cartesian closed category. Formalizing the conceptual view that polynomials are constructed from sums and products, we characterize this category in terms of the composite of the pseudomonads which freely add fibred sums and products to fibrations. The composite pseudomonad structure corresponds to a pseudo-distributive law between these two pseudomonads, which exists if and only if the base category is locally cartesian closed.

Keywords: polynomial functor, fibration, pseudo-distributive law, lax-idempotent monad, locally cartesian closed category, 2-bicategory

2010 MSC: {18C20, 18D30, 18D05

Theory and Applications of Categories, Vol. 33, 2018, No. 36, pp 1111-1144.

Published 2018-11-06.


TAC Home