Category-theoretic models of linear Abadi & Plotkin logic.

Birkedal, Lars; Møgelberg, Rasmus E.; Petersen, Rasmus L.

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A logic of orthogonality

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A logic of orthogonality characterizes all “orthogonality consequences" of a given class $Σ$ of morphisms, i.e. those morphisms $s$ such that every object orthogonal to $Σ$ is also orthogonal to $s$ . A simple four-rule deduction system is formulated which is sound in every cocomplete category. In locally presentable categories we prove that the deduction system is also complete (a) for all classes $Σ$ of morphisms such that all members except a set are regular epimorphisms and (b) for all classes...