English

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