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A logic of orthogonality

Jiří AdámekMichel HébertLurdes Sousa — 2006

Archivum Mathematicum

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 Σ , without...

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