Categorification of Algebras: 2-Algebras

Authors : İbrahim AKÇA, Ummahan EGE ARSLAN

Pages : 1-19

Doi:10.54286/ikjm.1183609

View : 82 | Download : 94

Publication Date : 2023-08-22

Article Type : Research Paper

Abstract :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.
Keywords : 2 categories, Crossed modules, Homotopy