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Complete Cuboidal Sets in Axiomatic Domain Theory (Extended Abstract)
 In Proceedings of 12th Annual Symposium on Logic in Computer Science
, 1997
"... ) Marcelo Fiore !mf@dcs.ed.ac.uk? Gordon Plotkin y !gdp@dcs.ed.ac.uk? John Power !ajp@dcs.ed.ac.uk? Department of Computer Science Laboratory for Foundations of Computer Science University of Edinburgh, The King's Buildings Edinburgh EH9 3JZ, Scotland Abstract We study the enrichme ..."
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) Marcelo Fiore !mf@dcs.ed.ac.uk? Gordon Plotkin y !gdp@dcs.ed.ac.uk? John Power !ajp@dcs.ed.ac.uk? Department of Computer Science Laboratory for Foundations of Computer Science University of Edinburgh, The King's Buildings Edinburgh EH9 3JZ, Scotland Abstract We study the enrichment of models of axiomatic domain theory. To this end, we introduce a new and broader notion of domain, viz. that of complete cuboidal set, that complies with the axiomatic requirements. We show that the category of complete cuboidal sets provides a general notion of enrichment for a wide class of axiomatic domaintheoretic structures. Introduction The aim of Axiomatic Domain Theory (ADT) is to provide a conceptual understanding of why domains are adequate as mathematical models of computation. (For a discussion see [12, x Axiomatic Domain Theory ].) The approach taken is to axiomatise the structure needed on a category so that its objects can be considered as domains, and its maps as continuous...
On braided tensor categories of type BCD
 J. reine angew. Math
"... Abstract. We give a full classification of all braided semisimple tensor categories whose Grothendieck semiring is the one of Rep ` O(∞) ´ (formally), Rep ` O(N) ´ , Rep ` Sp(N) ´ or of one of its associated fusion categories. If the braiding is not symmetric, they are completely determined by th ..."
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Abstract. We give a full classification of all braided semisimple tensor categories whose Grothendieck semiring is the one of Rep ` O(∞) ´ (formally), Rep ` O(N) ´ , Rep ` Sp(N) ´ or of one of its associated fusion categories. If the braiding is not symmetric, they are completely determined by the eigenvalues of a certain braiding morphism, and we determine precisely which values can occur in the various cases. If the category allows a symmetric braiding, it is essentially determined by the dimension of the object corresponding to the vector representation. 1.
Localization theory for triangulated categories
 In Triangulated categories, volume 375 of London Math. Soc. Lecture Note Ser
, 2010
"... 2. Categories of fractions and localization functors 3 3. Calculus of fractions 9 4. Localization for triangulated categories 14 ..."
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2. Categories of fractions and localization functors 3 3. Calculus of fractions 9 4. Localization for triangulated categories 14
Quantum logic in dagger kernel categories
 Order
"... This paper investigates quantum logic from the perspective of categorical logic, and starts from minimal assumptions, namely the existence of involutions/daggers and kernels. The resulting structures turn out to (1) encompass many examples of interest, such as categories of relations, partial inject ..."
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This paper investigates quantum logic from the perspective of categorical logic, and starts from minimal assumptions, namely the existence of involutions/daggers and kernels. The resulting structures turn out to (1) encompass many examples of interest, such as categories of relations, partial injections, Hilbert spaces (also modulo phase), and Boolean algebras, and (2) have interesting categorical/logical/ordertheoretic properties, in terms of kernel fibrations, such as existence of pullbacks, factorisation, orthomodularity, atomicity and completeness. For instance, the Sasaki hook and andthen connectives are obtained, as adjoints, via the existentialpullback adjunction between fibres. 1
Galois coverings, Morita equivalence and smash extensions of categories over a field
, 2005
"... We consider categories over a field k in order to prove that smash extensions and Galois coverings with respect to a finite group coincide up to Morita equivalence of kcategories. For this purpose we describe processes providing Morita equivalences called contraction and expansion. We prove that co ..."
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We consider categories over a field k in order to prove that smash extensions and Galois coverings with respect to a finite group coincide up to Morita equivalence of kcategories. For this purpose we describe processes providing Morita equivalences called contraction and expansion. We prove that composition of these processes provides any Morita equivalence, a result which is related with the karoubianisation (or idempotent completion) and additivisation of a kcategory.
An Axiomatic Setup for Algorithmic Homological Algebra and an Alternative Approach to Localization
 Journal of Algebra and its Applications (arXiv:1003.1943). 17
"... ar ..."
Infinite Comatrix Corings
, 2004
"... We characterize the corings whose category of comodules has a generating set of small projective comodules in terms of the (non commutative) descent theory. In order to extricate the structure of these corings, we give a generalization of the notions of comatrix coring and Galois comodule which avoi ..."
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Cited by 8 (3 self)
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We characterize the corings whose category of comodules has a generating set of small projective comodules in terms of the (non commutative) descent theory. In order to extricate the structure of these corings, we give a generalization of the notions of comatrix coring and Galois comodule which avoid finiteness conditions. A sufficient condition for a coring to be isomorphic to an infinite comatrix coring is found. We deduce in particular that any coalgebra over a field and the coring associated to a groupgraded ring are isomorphic to adequate infinite comatrix corings. We also characterize when the free module canonically associated to a (not necessarily finite) set of group like elements is Galois.
Locally Well Generated Homotopy Categories of Complexes
 DOCUMENTA MATH.
, 2010
"... ... That is, any localizing subcategory L in K(B) which is generated by a set is well generated in the sense of Neeman. We also show that K(B) itself being well generated is equivalent to B being pure semisimple, a concept which naturally generalizes right pure semisimplicity of a ring R for B = Mod ..."
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... That is, any localizing subcategory L in K(B) which is generated by a set is well generated in the sense of Neeman. We also show that K(B) itself being well generated is equivalent to B being pure semisimple, a concept which naturally generalizes right pure semisimplicity of a ring R for B = ModR.