## Hypernormalisation and linear exponential monads

### Richard Garner – 24 October 2018

In my seminar talk of 7 March this year, I gave various viewpoints on Jacobs' notion of "hypernormalisation" for probability distributions. In this talk, I explain that, really, the correct setting for hypernormalisation is a symmetric monoidal category endowed with a linear exponential monad (in the sense of linear logic). I use this to give various examples of hypernormalisation going beyond Jacobs' original setting. I conjecture that the finitely additive probability distribution monad on the category of sets is terminal among linear exponential monads with respect to the "convex" monoidal structure on Set.

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