| Title:
|
Polygraphs and discrete Conduché $\omega$-functors (English) |
| Author:
|
Guetta, Léonard |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
4 |
| Issue:
|
2 |
| Year:
|
2020 |
| Pages:
|
134-166 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We define a class of morphisms between strict $\omega$-categories called discrete Conduché $\omega$-functors that generalize discrete Conduché functors between categories and we study their properties related to polygraphs. The main result we prove is that for every discrete Conduché $\omega$-functor $f:C\rightarrow D$, if $D$ is a free strict $\omega$-category on a polygraph then so is $C$. (English) |
| Keyword:
|
Polygraphs |
| Keyword:
|
computads |
| Keyword:
|
strict $\omega$-categories |
| Keyword:
|
Conduché functors |
| MSC:
|
18N30 |
| idZBL:
|
Zbl 1467.18044 |
| idMR:
|
MR4133165 |
| DOI:
|
10.21136/HS.2020.11 |
| . |
| Date available:
|
2026-03-12T12:56:08Z |
| Last updated:
|
2026-03-12 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153427 |
| . |
| Reference:
|
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| Reference:
|
[2] Conduché, François: Au sujet de l’existence d’adjoints à droite aux foncteurs “image réciproque” dans la catégorie des catégories..C. R. Acad. Sci. Paris, 275:A891–894 |
| Reference:
|
[3] Giraud, Jean: Méthode de la descente..Société Mathématique de France |
| Reference:
|
[4] Guetta, Léonard: Homology of categories via polygraphic resolutions, 2020..arxiv:arXiv:2003.10734 http://arxiv.org/pdf/arXiv:2003.10734 |
| Reference:
|
[5] Hopcroft, John E, Ullman, : Introduction to automata theory, languages, and computation..Addison-Wesley |
| Reference:
|
[6] Lafont, Yves, Métayer, François: Polygraphic resolutions and homology of monoids..Journal of Pure and Applied Algebra, 213(6):947–968 |
| Reference:
|
[7] Lafont, Yves, Métayer, François, Worytkiewicz, Krzysztof: A folk model structure on omega-cat..Advances in Mathematics, 224(3):1183–1231 |
| Reference:
|
[8] Makkai, Michael: The word problem for computads.Available on the author’s web page http://www.math.mcgill.ca/makkai |
| Reference:
|
[9] Métayer, François: Resolutions by polygraphs..Theory and Applications of Categories, 11(7):148–184 |
| Reference:
|
[10] Métayer, François: Cofibrant objects among higher-dimensional categories..Homology, Homotopy and Applications, 10(1):181–203 |
| Reference:
|
[11] Street, Ross: Limits indexed by category-valued 2-functors..Journal of Pure and Applied Algebra, 8(2):149–181 |
| Reference:
|
[12] Street, Ross: Categorical structures..Handbook of algebra, 1:529–577 |
| . |
