Institution Morphisms

Institution Morphisms (2001)

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by Joseph Goguen , Grigore Rosu

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Datum	Value	Source
TITLE	1	SVM HeaderParse 0.1
AUTHOR NAME	Joseph Goguen	SVM HeaderParse 0.1
AUTHOR NAME	Grigore Rosu	SVM HeaderParse 0.1
ABSTRACT	Abstract. Institutions formalize the intuitive notion of logical system, including syntax, semantics, and the relation of satisfaction between them. Our exposition emphasizes the natural way that institutions can support deduction on sentences, and inclusions of signatures, theories, etc.; it also introduces terminology to clearly distinguish several levels of generality of the institution concept. A surprising number of dierent notions of morphism have been suggested for forming categories with institutions as objects, and an amazing variety of names have been proposed for them. One goal of this paper is to suggest a terminology that is uniform and informative to replace the current chaotic nomenclature; another goal is to investigate the properties and interrelations of these notions in a systematic way. Following brief expositions of indexed categories, diagram categories, twisted relations, and Kan extensions, we demonstrate and then exploit the duality between institution morphisms in the original sense of Goguen and Burstall, and the \plain maps " of Meseguer, obtaining simple uniform proofs of completeness and cocompleteness for both resulting categories. Because of this duality, we prefer the name \comorphism " over \plain map; " moreover, we argue that morphisms are more natural than comorphisms in many cases. We also consider \theoroidal " morphisms and comorphisms, which generalize signatures to theories, based on a theoroidal institution construction, nding that the \maps " of Meseguer are theoroidal comorphisms, while theoroidal morphisms are a new	SVM HeaderParse 0.1
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