Shapely monads and analytic functors

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

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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.

http://lama.univ-savoie.fr/~hirschowitz/

Olivier CHABROL
Posts created 14

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