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Algebraic Theories of Quasivarieties

✍ Scribed by Jiřı́ Adámek; Hans-E Porst

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
202 KB
Volume
208
Category
Article
ISSN
0021-8693

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✦ Synopsis

Analogously to the fact that Lawvere's algebraic theories of finitary varieties Ž . are precisely the small categories with finite products, we prove that i algebraic theories of many-sorted quasivarieties are precisely the small, left exact categories Ž . with enough regular injectives and ii algebraic theories of many-sorted Horn classes are precisely the small left exact categories with enough M M-injectives, where M M is a class of monomorphisms closed under finite products and containing all regular monomorphisms. We also present a Gabriel᎐Ulmer-type duality theory for quasivarieties and Horn classes.

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