Logic seminar

Speaker: Tslil Clingman, GWU

Title: An exploration of the category of relations

Abstract:  The category of relations, Rel, has a rich structure and serves as an important example of many concepts in the general theory. We will begin by understanding morphisms, limits and self-duality in this category, observing that one may take the external axiom of choice (as this is not always possible), before moving to understand any of the several important structural notions present in Rel. Depending on audience interest, we will see how Rel is a (closed) monoidal category, an enriched category (in two important ways) and even a strict 2-category. Finally, time permitting, we will explore a very important generalisation of Rel which leads to the general theory of weak 2-categories. Only elementary knowledge of category theory will be assumed.