Morita Equivalence for Many-Sorted Enriched Theories

Morita equivalence detects the situation in which two different theories admit the same class of models for the given theories. We generalise the result of Adámek, Sobral and Sousa concerning Morita equivalence of many-sorted algebraic theories. This generalisation is two-fold. We work in an enriche...

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Published in:Applied categorical structures 2016-12, Vol.24 (6), p.825-844
Main Authors: Dostál, Matĕj, Velebil, Jiří
Format: Article
Language:English
Subjects:
Convex and Discrete Geometry
Enrichment
Equivalence
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Theory of Computation
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description Morita equivalence detects the situation in which two different theories admit the same class of models for the given theories. We generalise the result of Adámek, Sobral and Sousa concerning Morita equivalence of many-sorted algebraic theories. This generalisation is two-fold. We work in an enriched setting, so the result is parametric in the choice of enrichment. Secondly, the result works for a reasonably general notion of a theory: the class of limits in the theory can be varied. As an example of an application of our result, we show enriched and many-sorted Morita equivalence results, and we recover the known results in the ordinary case.
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subjects Convex and Discrete Geometry
Enrichment
Equivalence
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Theory of Computation
title Morita Equivalence for Many-Sorted Enriched Theories
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