Canonical Gradings of Monads
Logic in Computer Science
2023-08-01 v1 Programming Languages
Category Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2307.16558,
title = {Canonical Gradings of Monads},
author = {Flavien Breuvart and Dylan McDermott and Tarmo Uustalu},
journal= {arXiv preprint arXiv:2307.16558},
year = {2023}
}
Comments
In Proceedings ACT 2022, arXiv:2307.15519