On classifying simplicial modules

ARVASİ Z., ILGAZ ÇAĞLAYAN E.

Communications in Algebra, vol.52, no.3, pp.945-959, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 52 Issue: 3
  • Publication Date: 2024
  • Doi Number: 10.1080/00927872.2023.2255266
  • Journal Name: Communications in Algebra
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.945-959
  • Keywords: Classifying simplicial module, (co)homology, crossed module, simplicial algebra, simplicial homotopy, CROSSED-MODULES, HOMOLOGY
  • Eskisehir Osmangazi University Affiliated: Yes

Abstract

In this paper, we prove that the classifying functors (Formula presented.) and (Formula presented.) are simplicially homotopy equivalent. Using this equivalency, we define classifying simplicial modules and give an alternative definition of (co)homology of crossed modules of algebras.