| Title:
|
Metric enrichment, finite generation, and the path coreflection (English) |
| Author:
|
Chirvasitu, Alexandru |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
60 |
| Issue:
|
2 |
| Year:
|
2024 |
| Pages:
|
61-99 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove a number of results involving categories enriched over CMet, the category of complete metric spaces with possibly infinite distances. The category CPMet of path complete metric spaces is locally $\aleph _1$-presentable, closed monoidal, and coreflective in CMet. We also prove that the category CCMet of convex complete metric spaces is not closed monoidal and characterize the isometry-$\aleph _0$-generated objects in CMet, CPMet and CCMet, answering questions by Di Liberti and Rosický. Other results include the automatic completeness of a colimit of a diagram of bi-Lipschitz morphisms between complete metric spaces and a characterization of those pairs (metric space, unital $C^*$-algebra) that have a tensor product in the CMet-enriched category of unital $C^*$-algebras. (English) |
| Keyword:
|
complete metric space |
| Keyword:
|
path metric |
| Keyword:
|
intrinsic metric |
| Keyword:
|
gluing |
| Keyword:
|
convex |
| Keyword:
|
monoidal closed |
| Keyword:
|
enriched |
| Keyword:
|
tensored |
| Keyword:
|
locally presentable |
| Keyword:
|
colimit |
| Keyword:
|
internal hom |
| MSC:
|
18A30 |
| MSC:
|
18C35 |
| MSC:
|
18D15 |
| MSC:
|
18D20 |
| MSC:
|
46L05 |
| MSC:
|
46L09 |
| MSC:
|
51F30 |
| MSC:
|
54E40 |
| MSC:
|
54E50 |
| idZBL:
|
Zbl 07830506 |
| idMR:
|
MR4729650 |
| DOI:
|
10.5817/AM2024-2-61 |
| . |
| Date available:
|
2024-04-04T12:02:35Z |
| Last updated:
|
2024-08-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152306 |
| . |
| Reference:
|
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