Internal categories

Adrian Miranda – 21 November 2018

If E is a category with finite limits, then categories, functors and natural transformations can be made sense of internally to E. The assignment of a finite limit category to the resulting 2-category Cat(E) extends to a 2-functor from finite limit categories to finite weighted limit 2-categories. This 2-functor has a left biadjoint given by the 'underlying finite limit category', and the resulting biadjunction is pseudocomonadic. We will also see a distributive law of this pseudocomonad over itself given by transposition of double categories, and two other monad like structures on the same 2-functor.

This talk will be based on my recently completed masters thesis.