John Dykes, Department of Pure Mathematics, University of Waterloo
"Putting the "Homotopy" in Homotopy Type Theory"
In this week's meeting of the Homotopy Type Theory Seminar, we begin by reviewing path induction. We then interpret Martin-Lof type theory in a homotopy-theoretic manner, viewing types as higher groupoids and functions as functors. We also discuss in detail how the notion of a homotopy between paths is related to identity types. Those who did not attend previous meetings are still encouraged to come!