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Retracting Some Paths in Process Algebra
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Geometry of Interaction and linear combinatory algebras
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Towards a quantum programming language
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A Categorical Semantics of Quantum Protocols
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Quantum circuit oracles for Abstract Machine computations
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From Coalgebraic to Monoidal Traces
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Representations of Petri net interactions
CONCUR'10 Proceedings of the 21st international conference on Concurrency theory
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We study structures which have arisen in recent work by the present author and Bob Coecke on a categorical axiomatics for Quantum Mechanics; in particular, the notion of strongly compact closed category. We explain how these structures support a notion of scalar which allows quantitative aspects of physical theory to be expressed, and how the notion of strong compact closure emerges as a significant refinement of the more classical notion of compact closed category. We then proceed to an extended discussion of free constructions for a sequence of progressively more complex kinds of structured category, culminating in the strongly compact closed case. The simple geometric and combinatorial ideas underlying these constructions are emphasized. We also discuss variations where a prescribed monoid of scalars can be ‘glued in' to the free construction.