Q-*-Categories

Hans Heymans

Research output: Contribution to journalArticle

10 Citations (Scopus)

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 languageEnglish
Pages (from-to)1-28
Number of pages28
JournalApplied Categorical Structures
Volume17
Publication statusPublished - 2009

Keywords

  • INVOLUTIVE QUANTALOID
  • TOPOS THEORY

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