| Title:
|
On inverse categories with split idempotents (English) |
| Author:
|
Schwab, Emil |
| Author:
|
Schwab, Emil Daniel |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
51 |
| Issue:
|
1 |
| Year:
|
2015 |
| Pages:
|
13-25 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present some special properties of inverse categories with split idempotents. First, we examine a Clifford-Leech type theorem relative to such inverse categories. The connection with right cancellative categories with pushouts is illustrated by simple examples. Finally, some basic properties of inverse categories with split idempotents and kernels are studied in terms of split idempotents which generate (right or left) principal ideals of annihilators. (English) |
| Keyword:
|
inverse categories |
| Keyword:
|
inverse monoids |
| Keyword:
|
split idempotents |
| Keyword:
|
pointed sets |
| Keyword:
|
annihilators |
| Keyword:
|
exact sequences |
| MSC:
|
18B40 |
| MSC:
|
20M50 |
| idZBL:
|
Zbl 06487018 |
| idMR:
|
MR3338763 |
| DOI:
|
10.5817/AM2015-1-13 |
| . |
| Date available:
|
2015-04-01T12:49:51Z |
| Last updated:
|
2016-04-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144231 |
| . |
| Reference:
|
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| Reference:
|
[2] Jones, D.G., Lawson, M.V.: Graph inverse semigroups: their characterization and completion.J. Algebra 409 (2014), 444–473. MR 3198850, 10.1016/j.jalgebra.2014.04.001 |
| Reference:
|
[3] Kastl, J.: Inverse categories.Studien zur Algebra und ihre Anwendungen, Akademie-Verlag Berlin, 1979, BAnd 7, pp. 51–60. Zbl 0427.18003, MR 0569574 |
| Reference:
|
[4] Kawahara, Y.: Relations in categories with pullbacks.Mem. Kyushu University, Series A, Math. 27 (1973), 149–173. Zbl 0261.18005, MR 0390017, 10.2206/kyushumfs.27.149 |
| Reference:
|
[5] Leech, J.: Constructing inverse monoids from small categories.Semigroup Forum 36 (1987), 89–116. Zbl 0634.18002, MR 0902733, 10.1007/BF02575008 |
| Reference:
|
[6] Mitchell, B.: Theory of categories.Acad. Press New York, 1965. Zbl 0136.00604, MR 0202787 |
| Reference:
|
[7] Schwab, E.: Image and inverse image mappings in exact inverse categories.Boll. U.M.I. 18–B (1981), 831–845. Zbl 0477.18002, MR 0641740 |
| Reference:
|
[8] Schwab, E., Schwab, E.D.: Quantum logic, dagger kernel categories and inverse Baer*-categories.Order 296 (2012), 405–417. MR 2979640, 10.1007/s11083-011-9211-7 |
| Reference:
|
[9] Schwab, E.D., Stoianov, G.: A Dirichlet analogue of the free monogenic inverse semigroup via Möbius inversion.Rocky Mountain J. Math 41 (2011), 1701–1710. Zbl 1233.20055, MR 2838084, 10.1216/RMJ-2011-41-5-1701 |
| . |
