Homotopy theory of stricter $n$-categories
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916980399800320 |
|---|---|
| author | Chanavat, Clémence |
| author_facet | Chanavat, Clémence |
| contents | We make strict $n$-categories even stricter by requiring they satisfy higher exchange laws governed by Hadzihasanovic's theory of regular directed complexes. We study the first properties of stricter $n$-categories, in particular, we define the Gray product, and prove stability under suspension, which is non-trivial. After reviewing and briefly expanding the theory diagrammatic sets and their associated model structures for $(\infty, n)$-categories, we construct a folk model structure on stricter $n$-categories, show that the walking equivalence coincides with the stricter polygraph generated by the walking equivalence in diagrammatic sets, and finally, that the folk model structure on stricter $n$-categories is right transferred from the diagrammatic model structure along a nerve construction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_26563 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homotopy theory of stricter $n$-categories Chanavat, Clémence Category Theory Algebraic Topology 18N30, 18N65, 18N40 We make strict $n$-categories even stricter by requiring they satisfy higher exchange laws governed by Hadzihasanovic's theory of regular directed complexes. We study the first properties of stricter $n$-categories, in particular, we define the Gray product, and prove stability under suspension, which is non-trivial. After reviewing and briefly expanding the theory diagrammatic sets and their associated model structures for $(\infty, n)$-categories, we construct a folk model structure on stricter $n$-categories, show that the walking equivalence coincides with the stricter polygraph generated by the walking equivalence in diagrammatic sets, and finally, that the folk model structure on stricter $n$-categories is right transferred from the diagrammatic model structure along a nerve construction. |
| title | Homotopy theory of stricter $n$-categories |
| topic | Category Theory Algebraic Topology 18N30, 18N65, 18N40 |
| url | https://arxiv.org/abs/2509.26563 |