The right-connected completion

Bryce Clarke – 29 June 2022

Right-connected double categories were first introduced by Bourke and Garner in the study of algebraic weak factorisation systems (AWFS). In this talk, I provide an explicit construction of the completion of a double category under the property of right-connectedness. Several properties of the right-connected completion are studied, including when its category of morphisms arises as a category of (co)algebras. If a double category has companions, it is also shown that its right-connected completion behaves like a lax limit in the 2-category of double categories, lax double functors, and horizontal transformations. Several examples will be presented throughout the talk, with a particular focus on applications to the theory of lenses.