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Polynomials, fibrations and distributive laws

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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.

http://www.tac.mta.ca/tac/volumes/33/36/33-36.pdf

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