| Title:
|
Dilatations of categories (English) |
| Author:
|
Mayeux, Arnaud |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
9 |
| Issue:
|
2 |
| Year:
|
2025 |
| Pages:
|
62-75 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Dilatations modify categories by imposing that some morphisms factorize through some others. This is formalized by a universal property. This text is devoted to introduce and study this construction. Examples of dilatations of categories include localizations of categories and dilatations of rings. (English) |
| Keyword:
|
dilatations of categories |
| Keyword:
|
factorizations of morphisms |
| Keyword:
|
fractions of morphisms |
| Keyword:
|
categories of fractions |
| Keyword:
|
localizations of categories |
| Keyword:
|
algebraic dilatations |
| Keyword:
|
universal property of dilatations |
| MSC:
|
18A05 |
| MSC:
|
18E35 |
| idMR:
|
MR4994250 |
| DOI:
|
10.21136/HS.2025.10 |
| . |
| Date available:
|
2026-03-13T14:49:41Z |
| Last updated:
|
2026-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153492 |
| . |
| Reference:
|
[1] Artin, M.: Non commutative rings..Class notes Math 251 Berkeley |
| Reference:
|
[2] Borceux, F.: Handbook of categorical algebra I Basic category theory..Encyclopedia of Mathematics and its Applications, 50. Cambridge University Press, Cambridge |
| Reference:
|
[3] Buan, A., Marsh, B.: From triangulated categories to module categories via localization II: calculus of fractions..J. London Math. Soc.(2) 86 152–170 MR 2959299, 10.1112/jlms/jdr077 |
| Reference:
|
[4] Dubouloz, A., Mayeux, A.: A polyptych of multi-centered deformation spaces,.Arxiv:2411.15606 http://arxiv.org/pdf/2411.15606 |
| Reference:
|
[5] Dubouloz, A., Mayeux, A., Santos, J.P. dos: A survey on algebraic dilatations,.Proceedings of the workshop “Langlands Program: Number Theory and Representation Theory”, BIRS-CMO |
| Reference:
|
[6] Duong, N. D., Hai, P. H., Santos, J. P. dos: On the structure of affine flat group schemes over discrete valuation rings, I..Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 18, no. 3, 977–1032 MR 3807593 |
| Reference:
|
[7] Gabriel, P., Zisman, M.: Calculus of fractions and homotopy theory..Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 35. New York: Springer-Verlag |
| Reference:
|
[8] Gelfand, S., Manin, Y.: Methods of homological algebra..Second edition. Springer Monographs in Mathematics. Springer-Verlag MR 1950475 |
| Reference:
|
[9] Mayeux, A.: Multi-centered dilatations, congruent isomorphisms and Rost double deformation space,.Transformation Groups. https://doi.org/10.1007/s00031-024-09894-9 10.1007/s00031-024-09894-9 |
| Reference:
|
[10] Mayeux, A., Richarz, T., Romagny, M.: Néron blowups and low-degree cohomological applications,.Algebr. Geom. 10, no. 6, 729–753 MR 4673395 |
| Reference:
|
[11] authors, The Stacks project: The Stacks Project..https://stacks.math.columbia.edu |
| . |
