Abstract Edward Prior

Title: Free EG-algebras on invertible objects

 Abstract:

 Many kinds of monoidal category are characterised by the presence of additional structure which is in some sense permutative - symmetries, braidings, etc. These types of categories are often amenable to a graphical description in the form of string diagrams, which allow us to use our geometric intuition to provide insight into purely algebraic problems. However, we sometimes want to work with invertible objects in these categories, but diagrams whose strings can cancel with one another are considerably harder to distinguish based on intuition alone.I will begin this talk by describing action operads, whose algebras can be used to formalise this notion of "monoidal categories with string-diagram-like structure". Then we will discuss how to construct the free such algebras on invertible objects, using the explicit example of braided monoidal categories.

 

References:

Nick Gurski, Operads, tensor products, and the categorical Borel construction (2015). https://arxiv.org/abs/1508.04050

Peter Selinger, A survey of graphical languages for monoidal categories (2009). https://arxiv.org/abs/0908.3347

 

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