Thursday, September 21, 2017, from 4 to 5:30pm
East Hall, room 3096
Speaker: Simon Cho (University of Michigan)
Title: A Category Theoretic Perspective on Continuous Logic
Although classical model theory is largely formulated in terms of the framework of sets, there is a rich theory that casts model theoretic structures in a category theoretic setting, a project which began with Lawvere’s thesis on “functorial semantics of algebraic theories” and has since grown into an important subfield of category theory. This interface between classical model theory and category theory continues to be an active area of research today.
In parallel, Lawvere also showed that structures – such as metric spaces – seemingly unrelated to categories arose naturally as examples of categories with appropriate enrichments V (for example V=R in the case of metric spaces). Now continuous logic/metric model theory is a generalization of classical model theory that, roughly, replaces sets with metric spaces and equality with the metric; a natural question to ask is whether the above perspective on metric spaces combines with the way of interpreting classical logic into category theory to produce a way to interpret continuous logic into enriched category theory. This talk will answer this in the affirmative, under reasonable conditions. The talk will make every effort to be self-contained, and as such will assume little to no prior knowledge of category theory.