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.
| Original language | English |
|---|---|
| Pages (from-to) | 1-28 |
| Number of pages | 28 |
| Journal | Applied Categorical Structures |
| Volume | 17 |
| Publication status | Published - 2009 |
Keywords
- INVOLUTIVE QUANTALOID
- TOPOS THEORY