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Approximation in quantaleenriched categories
 DIRK HOFMANN AND PAWE L WASZKIEWICZ
, 2010
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Qmodules are Qsuplattices
, 2007
"... It is well known that the internal suplattices in the topos of sheaves on a locale are precisely the modules on that locale. Using enriched category theory and a lemma on KZ doctrines we prove (the generalization of) this fact in the case of ordered sheaves on a small quantaloid. Comparing moduleequ ..."
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It is well known that the internal suplattices in the topos of sheaves on a locale are precisely the modules on that locale. Using enriched category theory and a lemma on KZ doctrines we prove (the generalization of) this fact in the case of ordered sheaves on a small quantaloid. Comparing moduleequivalence with sheafequivalence for quantaloids and using the notion of centre of a quantaloid, we refine a result of F. Borceux and E. Vitale. 1.
Contents
, 2006
"... Hardy and BMO spaces associated to divergence form elliptic operators ..."
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QMODULES ARE QSUPLATTICES
"... Abstract. It is well known that the internal suplattices in the topos of sheaves on a locale are precisely the modules on that locale. Using enriched category theory and a lemma on KZ doctrines we prove (the generalization of) this fact in the case of ordered sheaves on a small quantaloid. Comparing ..."
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Abstract. It is well known that the internal suplattices in the topos of sheaves on a locale are precisely the modules on that locale. Using enriched category theory and a lemma on KZ doctrines we prove (the generalization of) this fact in the case of ordered sheaves on a small quantaloid. Comparing moduleequivalence with sheafequivalence for quantaloids and using the notion of centre of a quantaloid, we refine a result of F. Borceux and E. Vitale. 1.
Abstract MFPS XX1 Preliminary Version Towards “dynamic domains”: totally continuous cocomplete Qcategories
"... It is common practice in both theoretical computer science and theoretical physics to describe the (static) logic of a system by means of a complete lattice. When formalizing the dynamics of such a system, the updates of that system organize themselves quite naturally in a quantale, or more generall ..."
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It is common practice in both theoretical computer science and theoretical physics to describe the (static) logic of a system by means of a complete lattice. When formalizing the dynamics of such a system, the updates of that system organize themselves quite naturally in a quantale, or more generally, a quantaloid. In fact, we are lead to consider cocomplete quantaloidenriched categories as fundamental mathematical structure for a dynamic logic common to both computer science and physics. Here we explain the theory of totally continuous cocomplete categories as generalization of the wellknown theory of totally continuous suplattices. That is to say, we undertake some first steps towards a theory of “dynamic domains”.
CATEGORIES ENRICHED OVER A QUANTALOID: ALGEBRAS
"... Abstract. Given a small quantaloid Q with a set of objects Q0, it is proved that complete skeletal Qcategories, completely distributive skeletal Qcategories, and Qpowersets of Qtyped sets are all monadic over the slice category of Set over Q0. 1. ..."
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Abstract. Given a small quantaloid Q with a set of objects Q0, it is proved that complete skeletal Qcategories, completely distributive skeletal Qcategories, and Qpowersets of Qtyped sets are all monadic over the slice category of Set over Q0. 1.