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Towards `dynamic domains': totally continuous cocomplete Qcategories, Theoret
 Comput. Sci
, 2007
"... Abstract. 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 mor ..."
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Cited by 4 (2 self)
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Abstract. 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”.
2007a), Components, Complements and the Reflection Formula, Theory and
"... ABSTRACT. Some basic features of the simultaneous inclusion of discrete fibrations and discrete opfibrations in categories over a base category X are considered. In particular, we illustrate the formulas (↓P)x = ten(x/X, P) ; (P↓)x = hom(X/x, P) ..."
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Cited by 3 (3 self)
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ABSTRACT. Some basic features of the simultaneous inclusion of discrete fibrations and discrete opfibrations in categories over a base category X are considered. In particular, we illustrate the formulas (↓P)x = ten(x/X, P) ; (P↓)x = hom(X/x, P)
Notions of Lawvere theory
"... Categorical universal algebra can be developed either using Lawvere theories (singlesorted finite product theories) or using monads, and the category of Lawvere theories is equivalent to the category of finitary monads on Set. We show how this equivalence, and the basic results of ..."
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Cited by 3 (0 self)
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Categorical universal algebra can be developed either using Lawvere theories (singlesorted finite product theories) or using monads, and the category of Lawvere theories is equivalent to the category of finitary monads on Set. We show how this equivalence, and the basic results of
2007), Components, Complements and Reflection Formulas, preprint
"... Abstract. We illustrate the formula (↓p)x = Γ!(x/p), which gives the reflection ↓p of a category p: P → X over X in discrete fibrations. One of its proofs is based on a “complement operator ” which takes a discrete fibration A to the functor ¬A, right adjoint to Γ!(A × −) : Cat/X → Set and valued in ..."
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Cited by 1 (1 self)
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Abstract. We illustrate the formula (↓p)x = Γ!(x/p), which gives the reflection ↓p of a category p: P → X over X in discrete fibrations. One of its proofs is based on a “complement operator ” which takes a discrete fibration A to the functor ¬A, right adjoint to Γ!(A × −) : Cat/X → Set and valued in discrete opfibrations. Some consequences and applications are presented. 1.
RELATIVE INJECTIVITY AS COCOMPLETENESS FOR A CLASS OF DISTRIBUTORS
"... Dedicated to Walter Tholen on the occasion of his sixtieth birthday ..."
DUALITY FOR CCD LATTICES
"... Abstract. The 2category of constructively completely distributive lattices is shown to be bidual to a 2category of generalized orders that admits a monadic schizophrenic object biadjunction over the 2category of ordered sets. 1. ..."
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Abstract. The 2category of constructively completely distributive lattices is shown to be bidual to a 2category of generalized orders that admits a monadic schizophrenic object biadjunction over the 2category of ordered sets. 1.