Toward compact double categories: Part 2

Last time we framed the puzzle of axiomatizing categorical duality and introduced new double-categorical tools, culminating with the twisted Hom functor. We’ll now get straight to the point by proposing a definition of a compact double category. After that we’ll fill in a few remaining technical details. More interestingly, we will examine the key examples and find that in all cases a compact double category, unlike a compact bicategory, uniquely determines the dual objects up to equivalence, even isomorphism.


This is a companion discussion topic for the original entry at https://topos.site/blog/2024-06-24-compact-double-categories-2/