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The Tile Model
 PROOF, LANGUAGE AND INTERACTION: ESSAYS IN HONOUR OF ROBIN MILNER
, 1996
"... In this paper we introduce a model for a wide class of computational systems, whose behaviour can be described by certain rewriting rules. We gathered our inspiration both from the world of term rewriting, in particular from the rewriting logic framework [Mes92], and of concurrency theory: among the ..."
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Cited by 65 (24 self)
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In this paper we introduce a model for a wide class of computational systems, whose behaviour can be described by certain rewriting rules. We gathered our inspiration both from the world of term rewriting, in particular from the rewriting logic framework [Mes92], and of concurrency theory: among the others, the structured operational semantics [Plo81], the context systems [LX90] and the structured transition systems [CM92] approaches. Our model recollects many properties of these sources: first, it provides a compositional way to describe both the states and the sequences of transitions performed by a given system, stressing their distributed nature. Second, a suitable notion of typed proof allows to take into account also those formalisms relying on the notions of synchronization and sideeffects to determine the actual behaviour of a system. Finally, an equivalence relation over sequences of transitions is defined, equipping the system under analysis with a concurrent semantics, ...
Process and Term Tile Logic
, 1998
"... In a similar way as 2categories can be regarded as a special case of double categories, rewriting logic (in the unconditional case) can be embedded into the more general tile logic, where also sideeffects and rewriting synchronization are considered. Since rewriting logic is the semantic basis o ..."
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Cited by 33 (25 self)
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In a similar way as 2categories can be regarded as a special case of double categories, rewriting logic (in the unconditional case) can be embedded into the more general tile logic, where also sideeffects and rewriting synchronization are considered. Since rewriting logic is the semantic basis of several language implementation efforts, it is useful to map tile logic back into rewriting logic in a conservative way, to obtain executable specifications of tile systems. We extend the results of earlier work by two of the authors, focusing on some interesting cases where the mathematical structures representing configurations (i.e., states) and effects (i.e., observable actions) are very similar, in the sense that they have in common some auxiliary structure (e.g., for tupling, projecting, etc.). In particular, we give in full detail the descriptions of two such cases where (net) processlike and usual term structures are employed. Corresponding to these two cases, we introduce two ca...
Frobenius monads and pseudomonoids
 2CATEGORIES COMPANION 73
, 2004
"... Six equivalent definitions of Frobenius algebra in a monoidal category are provided. In a monoidal bicategory, a pseudoalgebra is Frobenius if and only i f it is star autonomous. Autonomous pseudoalgebras are also Frobenius. What i t means for a morphism of a bicategory to be a projective equivalenc ..."
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Cited by 19 (4 self)
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Six equivalent definitions of Frobenius algebra in a monoidal category are provided. In a monoidal bicategory, a pseudoalgebra is Frobenius if and only i f it is star autonomous. Autonomous pseudoalgebras are also Frobenius. What i t means for a morphism of a bicategory to be a projective equivalence is defined; this concept is related to "strongly separable " Frobenius algebras and "weak monoidal Morita equivalence". Wreath products of Frobenius algebras are discussed.
General reversibility
 In EXPRESS’06, ENTCS. Elsevier
, 2006
"... The first and the second author introduced reversible ccs (rccs) in order to model concurrent computations where certain actions are allowed to be reversed. Here we show that the core of the construction can be analysed at an abstract level, yielding a theorem of pure category theory which underlies ..."
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Cited by 9 (3 self)
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The first and the second author introduced reversible ccs (rccs) in order to model concurrent computations where certain actions are allowed to be reversed. Here we show that the core of the construction can be analysed at an abstract level, yielding a theorem of pure category theory which underlies the previous results. This opens the way to several new examples; in particular we demonstrate an application to Petri nets. 1
An Australian conspectus of higher categories

, 2004
"... Much Australian work on categories is part of, or relevant to, the development of higher categories and their theory. In this note, I hope to describe some of the origins and achievements of our efforts that they might perchance serve as a guide to the development of aspects of higherdimensional wo ..."
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Cited by 6 (0 self)
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Much Australian work on categories is part of, or relevant to, the development of higher categories and their theory. In this note, I hope to describe some of the origins and achievements of our efforts that they might perchance serve as a guide to the development of aspects of higherdimensional work. I trust that the somewhat autobiographical style will add interest rather than be a distraction. For so long I have felt rather apologetic when describing how categories might be helpful to other mathematicians; I have often felt even worse when mentioning enriched and higher categories to category theorists. This is not to say that I have doubted the value of our work, rather that I have felt slowed down by the continual pressure to defend it. At last, at this meeting, I feel justified in speaking freely amongst motivated researchers who know the need for the subject is well established. Australian Category Theory has its roots in homology theory: more precisely, in the treatment of the cohomology ring and the Künneth formulas in the book by Hilton and Wylie [HW]. The first edition of the book had a mistake concerning the cohomology ring of a product. The Künneth formulas arise from splittings of the natural short exact sequences
Subobject Transformation Systems
, 2008
"... Subobject transformation systems (STS) are proposed as a novel formal framework for the analysis of derivations of transformation systems based on the algebraic, doublepushout (DPO) approach. They can be considered as a simplified variant of DPO rewriting, acting in the distributive lattice of subo ..."
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Cited by 6 (4 self)
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Subobject transformation systems (STS) are proposed as a novel formal framework for the analysis of derivations of transformation systems based on the algebraic, doublepushout (DPO) approach. They can be considered as a simplified variant of DPO rewriting, acting in the distributive lattice of subobjects of a given object of an adhesive category. This setting allows a direct analysis of all possible notions of dependency between any two productions without requiring an explicit match. In particular, several equivalent characterizations of independence of productions are proposed, as well as a local Church–Rosser theorem in the setting of STS. Finally, we show how any derivation tree in an ordinary DPO grammar leads to an STS via a suitable construction and show that relational reasoning in the resulting STS is sound and complete with respect to the independence in the original derivation tree.
Section Headings ¤1. Outline of the program
, 1995
"... subject which might be called postmodern algebra (or even Òpostmodern mathematicsÓ ..."
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subject which might be called postmodern algebra (or even Òpostmodern mathematicsÓ
University of Wales,
, 2001
"... Multiple categories: the equivalence of a globular and a cubical approach ..."
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Multiple categories: the equivalence of a globular and a cubical approach
and
, 2000
"... We show the equivalence of two kinds of strict multiple category, namely the wellknown globular ocategories, and the cubical ocategories with connections. # 2002 ..."
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We show the equivalence of two kinds of strict multiple category, namely the wellknown globular ocategories, and the cubical ocategories with connections. # 2002