| Title:
|
Totality of product completions (English) |
| Author:
|
Adámek, Jiří |
| Author:
|
Sousa, Lurdes |
| Author:
|
Tholen, Walter |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
41 |
| Issue:
|
1 |
| Year:
|
2000 |
| Pages:
|
9-24 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Categories whose Yoneda embedding has a left adjoint are known as total categories and are characterized by a strong cocompleteness property. We introduce the notion of multitotal category $\Cal A$ by asking the Yoneda embedding $\Cal A \rightarrow [\Cal A^{op},\Cal Set]$ to be right multiadjoint and prove that this property is equivalent to totality of the formal product completion $\Pi \Cal A$ of $\Cal A$. We also characterize multitotal categories with various types of generators; in particular, the existence of dense generators is inherited by the formal product completion iff measurable cardinals cannot be arbitrarily large. (English) |
| Keyword:
|
multitotal category |
| Keyword:
|
multisolid functor |
| Keyword:
|
formal product completion |
| MSC:
|
18A05 |
| MSC:
|
18A22 |
| MSC:
|
18A35 |
| MSC:
|
18A40 |
| idZBL:
|
Zbl 1034.18004 |
| idMR:
|
MR1756923 |
| . |
| Date available:
|
2009-01-08T18:58:02Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119137 |
| . |
| Reference:
|
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| . |
