A strengthened $(\infty, n)$-categorical pasting theorem
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917415468662784 |
|---|---|
| author | Chanavat, Clémence |
| author_facet | Chanavat, Clémence |
| contents | We extend Campion's pasting theorem for $(\infty, n)$-categories to a larger class of polygraphs, called the directed complexes with frame-acyclic molecules. It follows, for instance, that this pasting theorem applies to any polygraph presented by a semi-simplicial set, and that a large subclass of directed complexes with frame-acyclic molecules is compatible with the Gray tensor product. We also set up a comparison between directed complexes and Henry's regular polygraphs, and show that they coincide up to dimension $3$. As a corollary of our main results, the pasting theorem also applies to the class of regular $3$-polygraphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_22242 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A strengthened $(\infty, n)$-categorical pasting theorem Chanavat, Clémence Category Theory Algebraic Topology 18N65, 18N30, 18N20 We extend Campion's pasting theorem for $(\infty, n)$-categories to a larger class of polygraphs, called the directed complexes with frame-acyclic molecules. It follows, for instance, that this pasting theorem applies to any polygraph presented by a semi-simplicial set, and that a large subclass of directed complexes with frame-acyclic molecules is compatible with the Gray tensor product. We also set up a comparison between directed complexes and Henry's regular polygraphs, and show that they coincide up to dimension $3$. As a corollary of our main results, the pasting theorem also applies to the class of regular $3$-polygraphs. |
| title | A strengthened $(\infty, n)$-categorical pasting theorem |
| topic | Category Theory Algebraic Topology 18N65, 18N30, 18N20 |
| url | https://arxiv.org/abs/2603.22242 |