Length of fully faithful framed bicategories
Category Theory
2024-06-24 v3
Abstract
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.
Keywords
Cite
@article{arxiv.2402.16296,
title = {Length of fully faithful framed bicategories},
author = {Juan Orendain},
journal= {arXiv preprint arXiv:2402.16296},
year = {2024}
}
Comments
32 pages. Corrections in the form of improvements to v.2. New structural layout