Seminar

Test categories, first developed by Grothendieck, are categories whose presheaves can host a combinatorial model of the homotopy theory of spaces. The Homotopy Hypothesis suggests this equivalently describes a geometric model of infinity-groupoids, as in the example of simplicial sets, and to this effect Cisinski has shown that presheaves over a

(elegant local) test category model univalent type theory. This talk will cover background on test categories, show how all of the cube categories from the previous talk are test categories, and discuss why only some of them are strict test categories whose associated category of cubical sets models homotopy types and their cartesian products.

Zoom meeting ID: 930-5909-0699

Notes 13.2 MB application/pdf

Test Category Structure Of Cube Categories