Geodesic
Polynomials, fibrations and distributive laws
Theory and applications of categories, Tome 33 (2018), pp. 1111-1144

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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.

Publié le :
Classification : {18C20, 18D30, 18D05
Keywords: polynomial functor, fibration, pseudo-distributive law, lax-idempotent monad, locally cartesian closed category, 2-bicategory 
@article{TAC_2018_33_a35,
     author = {Tamara von Glehn},
     title = {Polynomials, fibrations and distributive laws},
     journal = {Theory and applications of categories},
     pages = {1111--1144},
     publisher = {mathdoc},
     volume = {33},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2018_33_a35/}
}
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Tamara von Glehn. Polynomials, fibrations and distributive laws. Theory and applications of categories, Tome 33 (2018), pp. 1111-1144. http://geodesic.mathdoc.fr/item/TAC_2018_33_a35/