Alexander Berenbeim, Department of Pure Mathematics, University of Waterloo
“What Is Equivalence?: An Introduction to weak ω-groupoids”
Higher category theory and higher groupoids are intimately connected, and at a minimum, the importance of this point of view is that n-categories allow us to avoid mistaking isomorphism for equality. Using certain simplicial sets with desirable properties, I will introduce the geometric definition of higher categories, and show how the choice of horn-fillers turns this geometric notion into an algebraic definition of ω groupoids. I will then develop the notion of a weak ω category as an algebra X for a contractible, normalized, globular operad P, and develop the notion of equivalence from this point of view, one can recover the notion of a weak ω groupoid using dual constructions.