Title
<tex>$Q-*-$</tex> categories <tex>$Q-*-$</tex> categories
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Dordrecht ,
Subject
Mathematics
Source (journal)
Applied categorical structures. - Dordrecht, 1993, currens
Volume/pages
17(2009) :1 , p. 1-28
ISSN
0927-2852
ISI
000262310700001
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
We consider the theory of categories enriched in an involutive quantaloid Q: the Q-*-categories. After giving an introduction to involutive quantaloids and nuclei, we use matrices with entries in Q to define Q-*-categories. Then we examine the relations between two kinds of morphisms between them, the functors and the *-maps, to provide a basis to study completeness properties. These results are used to provide a definition of pseudo-presheaves, presheaves and sheaves on involutive quantaloids in order to get a generalization of presheaves and sheaves on sites. Finally a characterization of these sheaves in terms of covers and compatible families is presented.
E-info
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