Title $Q-*-$ categories Author Heymans, Hans Faculty/Department Faculty of Sciences. Mathematics and Computer Science Publication type article Publication 2009 Dordrecht , 2009 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 https://repository.uantwerpen.be/docman/iruaauth/aae518/9ab1334.pdf http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000262310700001&DestLinkType=RelatedRecords&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000262310700001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000262310700001&DestLinkType=CitingArticles&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848 Handle