Action operads and invertibility
Nick Gurski (University of Sheffield)
Wednesday 11th February, 2015 16:00-17:00 Maths 516
Operads are a tool for parameterising the operations of an algebraic structure, and there are operads for monoids, rings and Lie algebras to name a few. But some operads have a different purpose, and these are the action operads of the title: they are families of groups whose role it is to carry natural automorphisms for other objects.
The canonical examples are the symmetric and braid groups. Invertible objects in monoidal categories are the generalisation of 1-dimensional vector spaces and line bundles to more general contexts. My goal in this talk will be to explain the connection between action operads and monoidal structures, and then compute the natural group actions on invertible objects using action operads. This is joint work with Ed Prior.