On classifying simplicial modules

Abstract

In this paper, we prove that the classifying functors $\overline{W}$ and $\mathit{Diag}°N$ 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.

Keywords:

• Classifying simplicial module
• (co)homology
• crossed module
• simplicial algebra
• simplicial homotopy

2020 Mathematics Subject Classification:

• 13C60
• 55R35
• 55R40
• 18N50