On 2-algebras: crossed R-modules and categorical R-algebras

Arvasi Z., Ilgaz Çağlayan E.

TURKISH JOURNAL OF MATHEMATICS, vol.45, no.3, pp.1319-1336, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 3
  • Publication Date: 2021
  • Doi Number: 10.3906/mat-2008-39
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1319-1336
  • Keywords: Category object, monoid object, categorical R-algebra, crossed R-module, simplicial R-algebra
  • Eskisehir Osmangazi University Affiliated: Yes

Abstract

In this work, we describe the category of categorical R-algebras and show that a categorical R-algebra is a category object in C = Alg(R). By using this property of categorical R-algebras, we can give an equivalency between the category of categorical R-algebras and the category of crossed R-modules and also the category of simplicial R-algebras.