Categorical structures enriched in a quantaloid: regular presheaves, regular semicategories
نویسنده
چکیده
Résumé. On étudie les préfaisceaux sur des semicatégories enrichies dans un quantalöide: cela donne lieu à la notion de préfaisceau régulier. Une semicatégorie est régulière si tous les préfaisceaux représentables sont réguliers, et ses préfaisceaux réguliers forment alors une (co)localistation essentielle de la catégorie de tous ses préfaisceaux. La notion de semidistributeur régulier permet d’établir l’équivalence de Morita des semicatégories régulières. Les ordres continus et les Ω-ensembles fournissent des exemples. Mots clés: quantalöide, semicatégorie, préfaisceau, régularité, équivalence de Morita, ordre continu, Ω-ensemble
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