Some notes on crossed semimodules


TEMEL S.

TURKISH JOURNAL OF MATHEMATICS, 2022 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Publication Date: 2022
  • Doi Number: 10.3906/mat-2110-44
  • Title of Journal : TURKISH JOURNAL OF MATHEMATICS
  • Keywords: Crossed semimodule, Schreier internal category, covering, action, lifting, simplicial monoid, MODULES, EXTENSIONS, CATEGORIES, GROUPOIDS, SPACES

Abstract

In this paper, we introduce the notion of lifting via a homomorphism of monoids for a crossed semimodule and give some properties. Further, we characterize actions and coverings of Schreier internal categories in the category MON of monoids and prove the natural equivalence between their categories. Then, we prove that liftings of a certain crossed semimodule are naturally equivalent to the actions of Schreier internal category in MON, where the Schreier internal category corresponds to the crossed semimodule. Finally, we give a relation between crossed semimodules and simplicial monoids.