| Title:
|
On fuzzification of the notion of quantaloid (English) |
| Author:
|
Solovyov, Sergey A. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
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0023-5954 |
| Volume:
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46 |
| Issue:
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6 |
| Year:
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2010 |
| Pages:
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1025-1048 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper considers a fuzzification of the notion of quantaloid of K. I. Rosenthal, which replaces enrichment in the category of $\bigvee$-semilattices with that in the category of modules over a given unital commutative quantale. The resulting structures are called quantale algebroids. We show that their constitute a monadic category and prove a representation theorem for them using the notion of nucleus adjusted for our needs. We also characterize the lattice of nuclei on a free quantale algebroid. At the end of the paper, we prove that the category of quantale algebroids has a monoidal structure given by tensor product. (English) |
| Keyword:
|
many-value topology |
| Keyword:
|
monadic category |
| Keyword:
|
nucleus |
| Keyword:
|
quantale |
| Keyword:
|
quantale algebra |
| Keyword:
|
quantale algebroid |
| Keyword:
|
quantale module |
| Keyword:
|
quantaloid |
| Keyword:
|
tensor product |
| MSC:
|
03E72 |
| MSC:
|
06F07 |
| MSC:
|
16G99 |
| MSC:
|
18A40 |
| MSC:
|
18B99 |
| idZBL:
|
Zbl 1218.06012 |
| idMR:
|
MR2797425 |
| . |
| Date available:
|
2011-04-12T12:49:36Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141464 |
| . |
| Reference:
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