# Categories of relations as models of quantum theory

@article{Heunen2015CategoriesOR, title={Categories of relations as models of quantum theory}, author={Chris Heunen and Sean Tull}, journal={ArXiv}, year={2015}, volume={abs/1506.05028} }

Categories of relations over a regular category form a family of models of quantum theory. Using regular logic, many properties of relations over sets lift to these models, including the correspondence between Frobenius structures and internal groupoids. Over compact Hausdorff spaces, this lifting gives continuous symmetric encryption. Over a regular Mal’cev category, this correspondence gives a characterization of categories of completely positive maps, enabling the formulation of quantum…

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