KOREAN JOURNAL OF MATHEMATICS, cilt.27, sa.2, ss.535-545, 2019 (ESCI)
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.