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352
Product systems over rightangled Artin semigroups
 Trans. Amer. Math. Soc
"... Abstract. We build upon MacLane’s definition of a tensor category to introduce the concept of a product system that takes values in a tensor groupoid G. We show that the existing notions of product systems fit into our categorical framework, as do the kgraphs of Kumjian and Pask. We then specializ ..."
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Abstract. We build upon MacLane’s definition of a tensor category to introduce the concept of a product system that takes values in a tensor groupoid G. We show that the existing notions of product systems fit into our categorical framework, as do the kgraphs of Kumjian and Pask. We then specialize to product systems over rightangled Artin semigroups; these are semigroups that interpolate between free semigroups and free abelian semigroups. For such a semigroup we characterize all product systems which take values in a given tensor groupoid G. In particular, we obtain necessary and sufficient conditions under which a collection of k 1graphs form the coordinate graphs of a kgraph.
A Relational Model of NonDeterministic Dataflow
 In CONCUR'98, volume 1466 of LNCS
, 1998
"... . We recast dataflow in a modern categorical light using profunctors as a generalisation of relations. The well known causal anomalies associated with relational semantics of indeterminate dataflow are avoided, but still we preserve much of the intuitions of a relational model. The development fits ..."
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Cited by 27 (13 self)
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. We recast dataflow in a modern categorical light using profunctors as a generalisation of relations. The well known causal anomalies associated with relational semantics of indeterminate dataflow are avoided, but still we preserve much of the intuitions of a relational model. The development fits with the view of categories of models for concurrency and the general treatment of bisimulation they provide. In particular it fits with the recent categorical formulation of feedback using traced monoidal categories. The payoffs are: (1) explicit relations to existing models and semantics, especially the usual axioms of monotone IO automata are read off from the definition of profunctors, (2) a new definition of bisimulation for dataflow, the proof of the congruence of which benefits from the preservation properties associated with open maps and (3) a treatment of higherorder dataflow as a biproduct, essentially by following the geometry of interaction programme. 1 Introduction A fundament...
Morita theory in abelian, derived and stable model categories, Structured ring spectra
 London Math. Soc. Lecture Note Ser
, 2004
"... These notes are based on lectures given at the Workshop on Structured ring spectra and ..."
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Cited by 27 (0 self)
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These notes are based on lectures given at the Workshop on Structured ring spectra and
Dbrane dynamics and Dbrane categories
 JHEP
"... This is a short nontechnical note summarizing the motivation and results of my recent work on Dbrane categories. I also give a brief outline of how this framework can be applied to study the dynamics of topological Dbranes and why this has a bearing on the homological mirror symmetry conjecture. T ..."
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Cited by 26 (12 self)
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This is a short nontechnical note summarizing the motivation and results of my recent work on Dbrane categories. I also give a brief outline of how this framework can be applied to study the dynamics of topological Dbranes and why this has a bearing on the homological mirror symmetry conjecture. This note can be read without any
The Group of EndoPermutation Modules
, 1998
"... The group D(P ) of all endopermutation modules for a finite pgroup P is a finitely generated abelian group. We prove that its torsionfree rank is equal to the number of conjugacy classes of noncyclic subgroups of P . We also obtain partial results on its torsion subgroup. We determine next the s ..."
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Cited by 26 (11 self)
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The group D(P ) of all endopermutation modules for a finite pgroup P is a finitely generated abelian group. We prove that its torsionfree rank is equal to the number of conjugacy classes of noncyclic subgroups of P . We also obtain partial results on its torsion subgroup. We determine next the structure of Q#D() viewed as a functor, which turns out to be a simple functor SE,Q , indexed by the elementary group E of order p and the trivial Out(E)module Q . Finally we describe a rather strange exact sequence relating Q#D(P ) , Q#B(P ) , and Q#R(P ) , where B(P ) is the Burnside ring and R(P ) is the Grothendieck ring of QP modules.
Normalization and the Yoneda Embedding
"... this paper we describe a new, categorical approach to normalization in typed  ..."
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Cited by 24 (3 self)
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this paper we describe a new, categorical approach to normalization in typed 
Doctrines Whose Structure Forms A Fully Faithful Adjoint String
 Theory Appl. Categ
, 1997
"... . We pursue the definition of a KZdoctrine in terms of a fully faithful adjoint string Dd a m a dD. We give the definition in any Graycategory. The concept of algebra is given as an adjunction with invertible counit. We show that these doctrines are instances of more general pseudomonads. The alge ..."
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Cited by 23 (5 self)
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. We pursue the definition of a KZdoctrine in terms of a fully faithful adjoint string Dd a m a dD. We give the definition in any Graycategory. The concept of algebra is given as an adjunction with invertible counit. We show that these doctrines are instances of more general pseudomonads. The algebras for a pseudomonad are defined in more familiar terms and shown to be the same as the ones defined as adjunctions when we start with a KZdoctrine. 1. Introduction Free cocompletions of categories under suitable classes of colimits were the motivating examples for the definition of KZdoctrines. We introduce in this paper a notstrict version of such doctrines defined via a fully faithful adjoint string. Thus, a nonstrict KZdoctrine on a 2category K consists of a normal endo homomorphism D : K \Gamma! K, and strong transformations d : 1K \Gamma! D, and m : DD \Gamma! D in such a way that Dd a m a dD forms a fully faithful adjoint string, satisfying one equation involving the unit of...
A uniqueness theorem for stable homotopy theory
 Math. Z
, 2002
"... Roughly speaking, the stable homotopy category of algebraic topology is obtained from the ..."
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Cited by 23 (10 self)
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Roughly speaking, the stable homotopy category of algebraic topology is obtained from the
Combinatorics of nonabelian gerbes with connection and curvature
, 2008
"... We give a functorial definition of Ggerbes over a simplicial complex when the local symmetry group G is nonAbelian. These combinatorial gerbes are naturally endowed with a connective structure and a curving. This allows us to define a fibered category equipped with a functorial connection over the ..."
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We give a functorial definition of Ggerbes over a simplicial complex when the local symmetry group G is nonAbelian. These combinatorial gerbes are naturally endowed with a connective structure and a curving. This allows us to define a fibered category equipped with a functorial connection over the space of edgepaths. By computing the curvature of the latter on the faces of an infinitesimal 4simplex, we recover the cocycle identities satisfied by the curvature of this gerbe. The link with BFtheories suggests that gerbes provide a framework adapted to the geometric formulation of strongly coupled gauge theories.