Philip Hackney: Induced model structures on cubical sets

Abstract

Quillen model categories are a particularly structured way to encode higher homotopical structure. It is advantageous to construct new model structures from existing ones, and there are a number of techniques to do so. For instance, if F: N → M is a functor with M a model category, it is sometimes possible to put a model structure on N where some parts of the structure lifted from the model structure on M. I'll explain simple criteria guaranteeing that such "induced" model structures exist in the special case when the functor F is both a right and a left adjoint. We'll apply these criteria to a category of cubical sets, giving model structures for ∞-groupoids and ∞-categories. This talk is based on joint work with Martina Rovelli.