Darien DeWolf (Saint Francis-Xavier)

*Restriction bicategories: two approaches*

**Abstract:**In this talk, I will introduce restriction bicategories: intuitively, a restriction bicategory is a bicategory B equipped with a family of functors r : B(A,B) --> B(A,A) which encode partiality in a way reminiscent of Cockett and Lack's restriction categories. Motivating this definition is the ``restriction bicategory'' of restriction bimodules.

Two approaches to defining such structures will be discussed:

(i) Cockett's approach has each restriction idempotent r(f) come with a monic
r(f) --> dom(f).

(ii) The approach taken in my thesis is more general in that it does not
require these monics.
Each approach has both merit and drawbacks, which will also be discussed.