Representability of Generalized Multicategories

Abstract: A multicategory has morphisms whose domains are lists of objects. A generalized multicategory has morphisms whose domains have a shape specified by a monad T. Representability concerns the equivalence between structure defined by universal property, and structure defined coherently: classically, this is Hermida’s equivalence between representable multicategories and monoidal categories. The theory of representability for generalized multicategories allow us to capture many results of this general shape. Seen through the lens of double category theory, to ask when a T-multicategory is representable is to ask when it is the underlying loose T-coalgebra of a pseudo-T-algebra. This talk will introduce the basic theory, such as the monadic adjunction between T-algebras and T-multicategories. This is based on work-in-progress with Nathanael Arkor.

category theory

Audience: researchers in the topic

Third Virtual Workshop on Double Categories