2016/04/20 by İbrahim İlker Akça, Akça, İbrahim İlker, Ummahan Ege Arslan +1
Computer Science · Decision Sciences · Mathematics · #18A05 #Advanced Algebra and Logic #Category Theory (math.CT) #FOS: Mathematics #Fuzzy and Soft Set Theory #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1604.05883
openalex publication_date 2016/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
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.