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On multivarieties and multialgebraic categories

✍ Scribed by Jiřı́ Adámek; Jiřı́ Rosický

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
157 KB
Volume
163
Category
Article
ISSN
0022-4049

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✦ Synopsis

Multivarieties are classes of algebras presented by exclusive-or's of equations. A full characterization of categories which are equivalent to multivarieties is presented, close to Lawvere's characterization of varieties. A comparison with Diers' concept of multialgebraic category is presented: this is precisely a multivariety with e ective equivalence relations. Besides, multialgebraic categories are shown to be precisely those categories which can be sketched by a (ÿnite product, coproduct)-sketch.

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## Abstract We study Gorenstein categories. We show that such a category has Tate cohomological functors and Avramov–Martsinkovsky exact sequences connecting the Gorenstein relative, the absolute and the Tate cohomological functors. We show that such a category has what Hovey calls an injective mod