Další seminář z algebry se koná 10.12.2020 od 13.00 online na platformě ZOOM. Informace pro připojení a další program semináře je zde.

John Bourke (Masaryk University)

Accessible Infinity-Cosmoi

Abstrakt:
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.