KOREAN JOURNAL OF MATHEMATICS, vol.27, no.2, pp.535-545, 2019 (ESCI)
Article / Article
KOREAN JOURNAL OF MATHEMATICS
Emerging Sources Citation Index (ESCI)
Crossed module, crossed semimodule, cat(1)-group, cat(1)-monoid, INTERNAL CATEGORIES, TOPOLOGICAL-GROUPS, CO-HOMOLOGY, MODULES, GROUPOIDS, EXTENSIONS
Recep Tayyip Erdoğan University Affiliated:
The main idea of this paper is to introduce the notion of cat(1)-monoids and to prove that the category of crossed semimodules C = (A, B, partial derivative) where A is a group is equivalent to the category of cat(1)-monoids. This is a generalization of the well known equivalence between category of cat(1)-groups and that of crossed modules over groups.