Flexible Presentations of Graded Monads
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.