Double categories versus factorization systems

Abstract: In the first part of the talk we will recall double categories and show that every orthogonal factorization system can be turned into a double category, every (nice) double category can be turned into an orthogonal factorization system, and that these processes are mutually inverse. We will do the same thing for strict factorization systems.

In the second part of the talk we will put the above results into a wider perspective of 2-category theory: if the double category is regarded as a diagram in Cat, producing the factorization system out of it amounts to taking a certain 2-categorial colimit of it (the codescent object). We will mention the connections to lax morphisms of algebras for a 2-monad, compositions of pinwheels, and possible extensions of the first part to weak factorization systems.

category theory

Audience: researchers in the topic

( video )

Second Virtual Workshop on Double Categories