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Description

Given a â globalâ monad, one wishes to obtain â localâ monads such that these locally behave like the global monad. In this talk, I will provide an overview of how subunits can be used to provide a notion of localisation on monads. I will start by introducing subunits, a special kind of subobject of the unit in a monoidal category. Afterwards, I will provide two equivalent ways of understanding the localisation of monads. The first involves a strength on subunits, while the second relies on the formal theory of graded monads. I will also explain how to construct one from the other.