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半群分次范畴的Smash积

DOI: 10.11830/ISSN.1000-5013.2008.03.0455

Keywords: 自由半群作用范畴, 商范畴, 半群分次范畴, Smash积

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Abstract:

设S为有单位元1的可消半群,引入半群S-分次范畴的Smash积的概念,分别证明半群S-分次范畴C的Smash积C#S的商范畴(C#S)/S与范畴C同构,以及自由半群S-范畴B的商范畴B/S的Smash积范畴(B/S)#S与范畴B同构.从而说明半群分次范畴的Smash积与自由半群作用范畴的商在半群分次范畴和自由半群作用范畴之间是互逆的结构.

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