Some notes on crossed semimodules

TEMEL S.

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

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 46
  • Basım Tarihi: 2022
  • Doi Numarası: 10.3906/mat-2110-44
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.768-784
  • Anahtar Kelimeler: Crossed semimodule, Schreier internal category, covering, action, lifting, simplicial monoid, MODULES, EXTENSIONS, CATEGORIES, GROUPOIDS, SPACES
  • Recep Tayyip Erdoğan Üniversitesi Adresli: Evet

Özet

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.