## Polynomial monads as fibred PROPs

### Richard Garner – 29 August 2018

We explain how polynomial monads on a category E can be represented as certain fibrations-with-structure over E which we term fibred PROPs. We also explain how this leads to semantics in non-cartesian settings such as the semantics for (finitary) polynomial monads on Set in symmetric monoidal categories. As is customary, the real explanation for all of this involves a non-standard enrichment.

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