Canonical Gradings of Monads
| Autor: | Breuvart, Flavien, McDermott, Dylan, Uustalu, Tarmo |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | EPTCS 380, 2023, pp. 1-21 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.4204/EPTCS.380.1 |
| Popis: | We define a notion of grading of a monoid T in a monoidal category C, relative to a class of morphisms M (which provide a notion of M-subobject). We show that, under reasonable conditions (including that M forms a factorization system), there is a canonical grading of T. Our application is to graded monads and models of computational effects. We demonstrate our results by characterizing the canonical gradings of a number of monads, for which C is endofunctors with composition. We also show that we can obtain canonical grades for algebraic operations. Comment: In Proceedings ACT 2022, arXiv:2307.15519 |
| Databáze: | arXiv |
| Externí odkaz: |
|