Shapely monads and analytic functors

Tom Hirschowitz
LAMA, Université Savoie Mont Blanc
https://www.lama.univ-savoie.fr/pagesmembres/hirschowitz/

Date(s) : 30/03/2017   iCal
11 h 00 min - 12 h 00 min

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.

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