Length of fully faithful framed bicategories
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913399211819008 |
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| author | Orendain, Juan |
| author_facet | Orendain, Juan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16296 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Length of fully faithful framed bicategories Orendain, Juan Category Theory 18N10 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. |
| title | Length of fully faithful framed bicategories |
| topic | Category Theory 18N10 |
| url | https://arxiv.org/abs/2402.16296 |