Categorification of Algebras: 2-Algebras
| Autor: | Akça, İbrahim İlker, Arslan, Ummahan Ege |
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| Rok vydání: | 2016 |
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| Druh dokumentu: | Working Paper |
| Popis: | This paper introduces a categorification of $k$-algebras called 2 -algebras, where k is a commutative ring. We define the 2-algebras as a 2-category with single object in which collections of all 1-morphisms and all 2-morphisms are k-algebras. It is shown that the category of 2 -algebras is equivalent to the category of crossed modules in commutative k -algebras. Also we define the notion of homotopy for 2-algebras and we explore the relations of crossed module homotopy and 2-algebra homotopy. Comment: 27 pages. arXiv admin note: text overlap with arXiv:math/0409602 by other authors |
| Databáze: | arXiv |
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