## A Consolidated Picture of Signed Measure Monads

### Hardy Hulley – 14 July 2021

Monads of probability measures, such as the distribution monad and the Giry monad, have received lots of attention in recent times. These monads are in fact sub-monads of more general signed measure monads, which despite being easier to understand, have not received any attention (as measure monads). For example, the distribution monad is a sub-monad of the familiar monad generated by the adjunction between sets and normed vector spaces, while the Giry monad is a sub-monad of the monad generated by the adjunction between measurable spaces and AL spaces. This talk will introduce the signed measure monads associated finitely supported discrete signed measures, countably supported discrete signed measures and arbitrary signed measures, with the role played by vector-valued integration in the definition of these monads highlighted.

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