Riehl and Verity introduced ∞-cosmoi – certain simplicially enriched categories – as a framework in which to give a model-independent approach to ∞-categories. For instance, there is an infinity cosmos of ∞-categories with finite limits or colimits, or of cartesian fibrations. In this talk, I will introduce the notion
of an accessible ∞-cosmos and explain that most, if not all, ∞-cosmoi arising in practice are accessible. Applying results of earlier work, it follows that accessible ∞-cosmoi have homotopy weighted colimits and admit a broadly applicable homotopical adjoint functor theorem.
This is a report on joint work with Steve Lack, and builds on recent work with Lack and Lukáš Vokřínek.
This video is part of Masaryk University‘s Algebra seminar.
