| Title:
|
A poset-like approach to positive opetopes (English) |
| Author:
|
Leclerc, Louise |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
9 |
| Issue:
|
2 |
| Year:
|
2025 |
| Pages:
|
76-102 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We introduce in this paper a new formalisation of positive opetopes where faces are organised in a poset. Then we show that our definition is equivalent to that of positives opetopes as given by Marek Zawadowski in [9]. (English) |
| Keyword:
|
opetopes |
| Keyword:
|
oriented graded poset |
| MSC:
|
06A07 |
| MSC:
|
06A11 |
| MSC:
|
06A75 |
| idMR:
|
MR4994251 |
| DOI:
|
10.21136/HS.2025.11 |
| . |
| Date available:
|
2026-03-13T14:50:18Z |
| Last updated:
|
2026-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153493 |
| . |
| Reference:
|
[1] Ara, Dimitri: Sur les infini-groupoïdes de grothendieck et une variante infini-catégorique.Thèse de doctorat dirigée par Maltsiniotis, Georges Mathématiques Paris 7 2010 |
| Reference:
|
[2] Baez, John C., Dolan, James: Higher-dimensional algebra III: N-categories and the algebra of opetopes.Advances in Mathematics, DOI:135(2):145–206 |
| Reference:
|
[3] Hadzihasanovic, Amar: A combinatorial-topological shape category for polygraphs.Applied Categorical Structures, Vol. 28, 419-476 MR 4089625, 10.1007/s10485-019-09586-6 |
| Reference:
|
[4] Kock, Joachim, Joyal, André, Batanin, Michael, Mascari, Jean-François: Polynomial functors and opetopes.Advances in Mathematics, Vol. 224, Iss. 6, 2690-2737, DOI:10.1016/j.aim.2010.02.012 MR 2652220, 10.1016/j.aim.2010.02.012 |
| Reference:
|
[5] Leinster, Tom: Higher operads, higher categories.Cambridge University Press |
| Reference:
|
[6] Palm, Thorsten: Dendrotopic sets for weak infinity-categories.Ph.D. - York University |
| Reference:
|
[7] Palm, Thorsten: Dendrotopic sets.Galois theory, hopf algebras, and semiabelian categories, pages 411-462, Fields institute communications 43 MR 2075598 |
| Reference:
|
[8] Thanh, Cédric Ho, Curien, Pierre-Louis, Mimram, Samuel: Type theoretical approaches to opetopes.Higher Structures, Vol. 6, 80-181 MR 4456593, 10.21136/HS.2022.02 |
| Reference:
|
[9] Zawadowski, Marek: On positive opetopes, positive opetopic cardinals and positive opetopic set.arXiv:0708.2658 |
| . |
