Some notes on crossed semimodules

TEMEL S.

TURKISH JOURNAL OF MATHEMATICS, vol.46, pp.768-784, 2022 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 46
  • Publication Date: 2022
  • Doi Number: 10.3906/mat-2110-44
  • 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.768-784
  • Keywords: Crossed semimodule, Schreier internal category, covering, action, lifting, simplicial monoid, MODULES, EXTENSIONS, CATEGORIES, GROUPOIDS, SPACES
  • Recep Tayyip Erdoğan University Affiliated: Yes

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.