Geodesic
2-dimensional bifunctor theorems and distributive laws
Theory and applications of categories, Tome 37 (2021), pp. 1149-1175.

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In this paper we consider the conditions that need to be satisfied by two families of pseudofunctors with a common codomain for them to be collated into a bifunctor. We observe similarities between these conditions and distributive laws of monads before providing a unified framework from which both of these results may be inferred. We do this by proving a version of the bifunctor theorem for lax functors. We then show that these generalised distributive laws may be arranged into a 2-category Dist(B, C, D), which is equivalent to Lax_op(B,Lax_op(C,D)). The collation of a distributive law into its associated bifunctor extends to a 2-functor into Lax_op(B x C, D), which corresponds to uncurrying via the aforementioned equivalence. We also describe subcategories on which collation itself restricts to an equivalence. Finally, we exhibit a number of natural categorical constructions as special cases of our result.
Publié le :
Classification : 18D05, 18C15
Keywords: morphism of bicategories, triple, braiding, curry, exponential 
@article{TAC_2021_37_a33,
     author = {Peter F. Faul and Graham Manuell and Jos\'e Siqueira},
     title = {2-dimensional bifunctor theorems and distributive laws},
     journal = {Theory and applications of categories},
     pages = {1149--1175},
     publisher = {mathdoc},
     volume = {37},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2021_37_a33/}
}
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Peter F. Faul; Graham Manuell; José Siqueira. 2-dimensional bifunctor theorems and distributive laws. Theory and applications of categories, Tome 37 (2021), pp. 1149-1175. http://geodesic.mathdoc.fr/item/TAC_2021_37_a33/