Flexible Presentations of Graded Monads

Dylan McDermott

Reykjavik University




Abstract: Graded monads are a generalization of monads that are used for example to track quantitative information in models of effects. I will talk about a further generalization that we call flexibly graded monads. These capture more graded structures, for example, graded monoids are the algebras of a flexibly graded monad, but are not the algebras of an ordinary graded monad. The motivation is to develop a flexible notion of presentation (by operations and equations) for (ordinary) graded monads. As part of this work, we reformulate graded monads and related concepts in terms of locally graded categories, which provide a nice setting for working with grading.

This is joint work with Shin-ya Katsumata, Tarmo Uustalu and Nicolas Wu.