2024/02/26 by Orendain, Juan
#18N10 #Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2402.16296
The length of a double category is a numerical invariant measuring the 'work' it takes to reconstruct the double category from its globular data. The smallest possible length of a double category is 1. It is conjectured that framed bicategories are of length 1. In this paper we prove this conjecture for a particular class of framed bicategories, namely for those double categories for which all their unit squares are cartesian/opcartesian. We call these framed bicategories fully faithful/absolutely dense.