TY - JOUR
T1 - Inner horns for 2-quasi-categories
AU - Maehara, Yuki
N1 - Funding Information:
The author would like to thank his supervisor Dominic Verity for helpful feedback on earlier versions of this paper. He also gratefully acknowledges the support of an International Macquarie University Research Training Program Scholarship (Allocation Number: 2017127 ). Thanks to the anonymous referees' comments, the readability of this paper has been greatly improved and an error in the original proof of Lemma 3.4 has been corrected.
Publisher Copyright:
© 2020 Elsevier Inc.
PY - 2020/3/25
Y1 - 2020/3/25
N2 - Dimitri Ara's 2-quasi-categories, which are certain presheaves over André Joyal's 2-cell category Θ2, are an example of a concrete model that realises the abstract notion of (∞,2)-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.
AB - Dimitri Ara's 2-quasi-categories, which are certain presheaves over André Joyal's 2-cell category Θ2, are an example of a concrete model that realises the abstract notion of (∞,2)-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.
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U2 - 10.1016/j.aim.2020.107003
DO - 10.1016/j.aim.2020.107003
M3 - Article
AN - SCOPUS:85078229596
SN - 0001-8708
VL - 363
JO - Advances in Mathematics
JF - Advances in Mathematics
M1 - 107003
ER -