Dinaturality for double categories

Abstract: We introduce dinatural transformations for double categories and show that they enjoy several of the same properties as dinatural transformations for 1-categories, including subsuming ordinary natural transformations, composing with them, and composing with one another in a suitably groupoidal setting. As an application, we show how extranatural transformations for 1-categories can be characterized using dinatural transformations in the double category of small categories.

category theory

Audience: researchers in the topic

Third Virtual Workshop on Double Categories