Centre for Mathematics, University of Coimbra

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Type:	Preprint
National /International:	International
Title:	A logic of orthogonality
Publication Date:	2006
Authors:	- Jirí Adámek - Michel Hébert - Lurdes Sousa
Abstract:	A logic of orthogonality characterizes all "orthogonality consequences" of a given class S of morphisms, i.e. those morphisms s such that every object orthogonal to S 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 S of morphisms such that all members except a set are regular epimorphisms and (b) for all classes S without restriction, under the set-theoretical assumption that Vopenka???s Principle holds. For finitary morphisms, i.e. morphisms with finitely presentable domains and codomains, an appropriate finitary logic is presented, and proved to be sound and complete; here the proof follows immediately from previous joint results of Jirí RosickÜ and the first two authors.
Institution:	DMUC 06-43
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