The model category of algebraically cofibrant 2-categories

Abstract: It is a commonplace of higher category theory that, while every weak 2-category is equivalent to a strict 2-category, not every weak 3-category is equivalent to a strict 3-category. Nevertheless, the coherence theorem of Gordon, Power, and Street states that every weak 3-category is equivalent to a Gray-category (that is, a category enriched over the category of 2-categories equipped with Gray's symmetric monoidal structure). However, there are certain fundamental obstructions to the development of a purely Gray-enriched model for three-dimensional category theory. These obstructions may be overcome by the introduction of a new base for enrichment with more satisfactory technical properties: the cartesian closed model category of algebraically cofibrant 2-categories, which is the subject of this talk.

In this talk, Alexander will construct the model category of algebraically cofibrant 2-categories and explore several of its excellent properties. In particular, he will prove that its full subcategory of fibrant-cofibrant objects is equivalent to the category of bicategories and normal pseudofunctors, and that it is cartesian closed as a model category.

 

In person attendance is available in HN 1.33 for up to 52 people.

All attendees will be asked to check in using the CBR Covid-safe Check-In app or sign in on arrival.

Zoom attenence is also avalible. 

To join this seminar via Zoom please click here.

If you would like to join the seminar online and are not currently affiliated with ANU, please contact Martin Helmer at martin.helmer@anu.edu.au.