| Title:
|
A logic of orthogonality (English) |
| Author:
|
Adámek, Jiří |
| Author:
|
Hébert, M. |
| Author:
|
Sousa, L. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
42 |
| Issue:
|
4 |
| Year:
|
2006 |
| Pages:
|
309-334 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A logic of orthogonality characterizes all “orthogonality consequences" of a given class $\Sigma $ of morphisms, i.e. those morphisms $s$ such that every object orthogonal to $\Sigma $ is also orthogonal to $s$. A simple four-rule deduction system is formulated which is sound in every cocomplete category. In locally presentable categories we prove that the deduction system is also complete (a) for all classes $\Sigma $ of morphisms such that all members except a set are regular epimorphisms and (b) for all classes $\Sigma $, without restriction, under the set-theoretical assumption that Vopěnka’s Principle holds. For finitary morphisms, i.e. morphisms with finitely presentable domains and codomains, an appropriate finitary logic is presented, and proved to be sound and complete; here the proof follows immediately from previous joint results of Jiří Rosický and the first two authors. (English) |
| MSC:
|
03C05 |
| MSC:
|
03G30 |
| MSC:
|
18C10 |
| MSC:
|
18C35 |
| idZBL:
|
Zbl 1156.18301 |
| idMR:
|
MR2283016 |
| . |
| Date available:
|
2008-06-06T22:48:43Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108011 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Adámek J., Rosický J.: Locally presentable and accessible categories.Cambridge University Press, 1994. Zbl 0795.18007, MR 1294136 |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
[10] Hébert M., Adámek J., Rosický J.: More on orthogonolity in locally presentable categories.Cahiers Topologie Géom. Différentielle Catég. 62 (2001), 51–80. MR 1820765 |
| Reference:
|
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| Reference:
|
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