\boldsymbol{\mathcal{Q}}-*-Categories |
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Authors: | Hans Heymans |
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Institution: | (1) Department of Mathematics and Computer Science, University of Antwerp, Middelheimlaan 1, 2020 Antwerp, Belgium |
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Abstract: | We consider the theory of categories enriched in an involutive quantaloid : the -*-categories. After giving an introduction to involutive quantaloids and nuclei, we use matrices with entries in to define -*-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.
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Keywords: | Involutive quantaloids Quantales Sheaves Nuclei Relations Matrices Topos theory |
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