## Tom Hirschowitz (LAMA, USMB/CNRS), Shapely monads and analytic functors

### Programme

- 30 mars 2017, 11:00 - 12:30

### Résumé

In this work, we give precise mathematical form to the idea of a structure whose data and axioms are faithfully represented by a graphical calculus; some prominent examples are operads, polycategories, properads, and PROPs. Building on the established presentation of such structures as algebras for monads on presheaf categories, we describe a characteristic property of the associated monads — the shapeliness of the title — which says that ‘any two operations of the same shape agree’. In fact, shapeliness also gives a way to define the data and axioms of a structure directly from its graphical calculus, by generating a free shapely monad on the basic operations of the calculus.

*This is joint work with Richard Garner.*