Department of Mathematics - Master Calendar

View Full Calendar

Maru Sarazola (Minnesota): Double categorical equivalences

Event Type
Seminar/Symposium
Sponsor
UIUC math department
Location
Altgeld
Date
Apr 22, 2025   11:00 am  
Views
201
Originating Calendar
Topology Seminar

Double categories are a flexible 2-dimensional setting that allows us to encode two types of morphisms between objects, as well as a notion of higher cells. Surprisingly, unlike most categorical structures, there is no canonical notion of "equivalence of double categories", as every possible definition requires us to make a choice. In this talk we will introduce double categories and illustrate the issue that arises when defining equivalences. Then, we will show how we can use homotopy theory to give a decisive answer as to who the "canonical double categorical equivalences" should be. In the process, we will show how to construct a plethora of model structures on double categories whose homotopy theories encode different 2-dimensional structures. Based on joint work with Lyne Moser and Paula Verdugo.

link for robots only