Categorification of Algebras: 2-Algebras

Year 2023, Volume: 5 Issue: 1, 1 - 19, 22.08.2023

İbrahim Akça , Ummahan Ege Arslan

https://doi.org/10.54286/ikjm.1183609

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.

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