We will continue online on Thursday, December 10th, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

John Bourke (Masaryk University)

Accessible Infinity-Cosmoi

Abstract:
Riehl and Verity introduced infinity-cosmoi - certain simplicially enriched categories - as a framework in which to give a model-independent approach to infinity categories.  For instance, there is an infinity cosmos of infinity-categories with finite limits or colimits, or of cartesian fibrations.  In this talk, I will introduce the notion of an accessible infinity-cosmos and explain that most, if not all, infinity-cosmoi arising in practise are accessible.  Applying results of earlier work, it follows that accessible infinity-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.