The \({\mathcal D}\)-category of a monoid (Q1088006)
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scientific article; zbMATH DE number 3989651
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The \({\mathcal D}\)-category of a monoid |
scientific article; zbMATH DE number 3989651 |
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The \({\mathcal D}\)-category of a monoid (English)
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1986
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The division category of a semigroup S, denoted by \({\mathcal D}(S)\) was introduced by the author [ibid. 11, 283-296 (1976; Zbl 0338.20094)]. In the present paper the author studies \({\mathcal D}(S)\) where S is a monoid. He finds conditions on S which ensure that (i) \({\mathcal D}(S)\) has an initial object, (ii) \({\mathcal D}(S)\) may be identified with the \({\mathcal J}\) quasiorder. He also examines the existence of terminal objects in \({\mathcal D}(S)\).
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Green's equivalence relations
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division category
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monoid
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initial object
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terminal objects
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