Inner horns for 2-quasi-categories
Category Theory
2020-03-26 v3 Algebraic Topology
Abstract
Dimitri Ara's 2-quasi-categories, which are certain presheaves over Andr\'{e} Joyal's 2-cell category , are an example of a concrete model that realises the abstract notion of -category. In this paper, we prove that the 2-quasi-categories and the fibrations into them can be characterised using the inner horn inclusions and the equivalence extensions introduced by David Oury. These maps are more tractable than the maps that Ara originally used and therefore our result can serve as a combinatorial foundation for the study of 2-quasi-categories.
Keywords
Cite
@article{arxiv.1902.08720,
title = {Inner horns for 2-quasi-categories},
author = {Yuki Maehara},
journal= {arXiv preprint arXiv:1902.08720},
year = {2020}
}
Comments
v3. 45 pages. Minor revision. Published version. [v2: Corrected an error in the proof of Lemma 3.4. Expanded/rewrote the proofs and added many pictures. Added a section on the Gray tensor product.]