Multi-groups

In the present paper we define homogeneous algebraic systems. Particular cases of these systems are semigroup (monoid, group) systems. These algebraic systems were studied by J. Loday, A. Zhuchok, T. Pirashvili, and N. Koreshkov. Quandle systems were introduced and studied by V. Bardakov, D. Fedoseev, and V. Turaev.
We construct some group systems on the set of square matrices over a field $\mathbb{K}$. Also, we define rack systems on the set $V \times G$, where $V$ is a vector space of dimension $n$ over $\mathbb{K}$ and $G$ is a subgroup of $GL_n(\mathbb{K})$. Finally, we find the connection between skew braces and dimonoids.