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.
Primary Language | English |
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Subjects | Mathematical Sciences |
Journal Section | Articles |
Authors | |
Early Pub Date | February 27, 2023 |
Publication Date | August 22, 2023 |
Acceptance Date | December 23, 2022 |
Published in Issue | Year 2023 Volume: 5 Issue: 1 |