2-dimensional bifunctor theorems and distributive laws
| Autor: | Faul, Peter F., Manuell, Graham, Siqueira, Jose |
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| Rok vydání: | 2020 |
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| Zdroj: | Theory Appl. Categ., 37(34):1149-1175, 2021 |
| Druh dokumentu: | Working Paper |
| Popis: | 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(B,Lax(C,D)). The collation of a distributive law into its associated bifunctor extends to a 2-functor into Lax($B \times C$, 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. Comment: 23 pages; Completely restructured the paper for greater clarity |
| Databáze: | arXiv |
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