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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Bibliographic Details
Published inApplied categorical structures Vol. 24; no. 6; pp. 825 - 844
Main Authors Dostál, Matĕj, Velebil, Jiří
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.12.2016
Springer Nature B.V
Subjects
Convex and Discrete Geometry
Enrichment
Equivalence
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Theory of Computation
MSC 18C10
MSC 18D20
Morita equivalence
Lawvere theory
Cauchy completion
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Summary: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.
ISSN:0927-2852
1572-9095
DOI:10.1007/s10485-015-9406-y