Totality of product completions
Adámek, Jiří ; Sousa, Lurdes ; Tholen, Walter
Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000), p. 9-24 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 2000-01-01
Classification:  18A05,  18A22,  18A35,  18A40 
@article{119137,
     author = {Ji\v r\'\i\ Ad\'amek and Lurdes Sousa and Walter Tholen},
     title = {Totality of product completions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {41},
     year = {2000},
     pages = {9-24},
     zbl = {1034.18004},
     mrnumber = {1756923},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119137}
}

Adámek, Jiří; Sousa, Lurdes; Tholen, Walter. Totality of product completions. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) pp. 9-24. http://gdmltest.u-ga.fr/item/119137/

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