| Title:
|
Unifying notions of pasting diagrams (English) |
| Author:
|
Forest, Simon |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
6 |
| Issue:
|
1 |
| Year:
|
2022 |
| Pages:
|
1-79 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this work, we relate the three main formalisms for the notion of pasting diagram in strict $\omega$: Street’s {\it parity complexes}, Johnson’s {\it pasting schemes} and Steiner’s {\it augmented directed complexes}. In the process, we show that the axioms of parity complexes and pasting schemes are not strong enough for them to correctly represent pasting diagrams, and we do so by providing a counter-example. Then, we introduce a new formalism, called {\it torsion-free complexes}, which aims at encompassing the three other ones. We prove its correctness by providing a detailed proof that an instance induces a free $\omega$-category. Next, we prove that the three other formalisms can be embedded in some sense in the new one. Finally, we show that there are no other embedding between these four formalisms. (English) |
| Keyword:
|
pasting diagrams |
| Keyword:
|
strict omega-categories |
| Keyword:
|
polygraphs |
| Keyword:
|
computads |
| Keyword:
|
parity complexes |
| Keyword:
|
pasting schemes |
| Keyword:
|
augmented |
| MSC:
|
18N30 |
| idZBL:
|
Zbl 1498.18033 |
| idMR:
|
MR4456592 |
| DOI:
|
10.21136/HS.2022.01 |
| . |
| Date available:
|
2026-03-13T09:54:41Z |
| Last updated:
|
2026-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153445 |
| . |
| Reference:
|
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| . |
