# The universal loop space operad and generalisations

The problem of modelling homotopy types by omega-groupoids has been approached in many different ways in recent years. I will discuss the theory proposed by Batanin/Leinster using globular operads. There are various analogies with the use of operads to study loop spaces; I will recall the loop space operad E called universal’’ by Salvatore, and the analogous globular operad G which can be used to recognise the fundamental \omega-groupoid of a space. I will give a categorical proof of the universal property of E, enabling generalisation to prove a universal property of G. The helps us identify other, more tractable, operads for fundamental \omega-groupoids.

This talk is part of the Category Theory Seminar series.