
Quantum channels as a categorical completion
We propose a categorical foundation for the connection between pure and ...
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Hypergraph Categories
Hypergraph categories have been rediscovered at least five times, under ...
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Quantifying coherence with quantum addition
Quantum addition channels have been recently introduced in the context o...
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Quantum Coherence Measures for Quantum Switch
We suppose that a structure working as a quantum switch will be a signif...
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Noncommutative coherence spaces for full linear logic
We propose a model of full propositional linear logic based on topologic...
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On bifibrations of model categories
In this article, we develop a notion of Quillen bifibration which combin...
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Order polarities
We define an order polarity to be a polarity (X,Y,R) where X and Y are p...
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Coherence for braided distributivity
In categorytheoretic models for the anyon systems proposed for topological quantum computing, the essential ingredients are two monoidal structures, ⊕ and ⊗. The former is symmetric but the latter is only braided, and ⊗ is required to distribute over ⊕. What are the appropriate coherence conditions for the distributivity isomorphisms? We came to this question working on a simplification of the categorytheoretical foundation of topological quantum computing, which is the intended application of the research reported here. This question above was answered by Laplaza when both monoidal structures are symmetric, but topological quantum computation depends crucially on ⊗ being only braided, not symmetric. We propose coherence conditions for distributivity in this situation, and we prove that our coherence conditions are (a) strong enough to imply Laplaza's when the latter are suitably formulated, and (b) weak enough to hold when  as in the categories used to model anyons  the additive structure is that of an abelian category and the braided ⊗ is additive. Working on these results, we also found a new redundancy in Laplaza's conditions.
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