Turkish Journal of Mathematics
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.
DOI
10.55730/1300-0098.3122
Keywords
Crossed semimodule, Schreier internal category, covering, action, lifting, simplicial monoid
First Page
768
Last Page
784
Recommended Citation
TEMEL, SEDAT
(2022)
"Some notes on crossed semimodules,"
Turkish Journal of Mathematics: Vol. 46:
No.
3, Article 7.
https://doi.org/10.55730/1300-0098.3122
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss3/7
