The environment, as a space shared between agents, is a key component of multi\-agent systems (MAS). Depending on systems, this space may integrate physical, communication or social dimensions. Each of them has its own process and rules to support agents' interaction. For instance, in the physical dimension, the rules may be based on the agents' location. The agents' interaction is then contextualized, and the environment allows a multi-agent control since it performs the interactions according to the state and rules of the MAS. The dimensions of the environment are generally connected either in an application-dependent ad-hoc way outside of the agents or within each agent. In order to ensure a multi-agent control, the relations between dimensions must be explicit outside of the agents. Using these relations between the environment dimensions, the interaction becomes also multi-dimensional. In this paper, we propose to formalize rules and mechanisms to make this connection outside of the agents and in a generic way.