Wednesday, November 26, 2014 — 2:30 PM EST

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.

Location 
MC - Mathematics & Computer Building
5046
200 University Avenue West

Waterloo, ON N2L 3G1
Canada

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