To federate is to create a collective which includes other collectives.
A federation is an alliance of collectives which recognize a coordinating collective.
Agents create a federation by developing a coordinating collective which governs specifications for other collectives to participate in, and potentially identify as a member of, the federation. Depending on the governance system of the federation, such member collectives might or might not be member-agents.
The definition above is intentionally generic. “Federation” has been applied to many complex alliances with varying traits. For example, the coordinating agent of a federation might require that member groups may act only as subordinate subgroups of the coordinating agent in some specific activities. However, some self-identified "federations" are alliances in which membership is (outside of extreme controversies) purely self-assigned, and in which the member collectives always act autonomously. Such alliances are not federations by this MOT definition.
Loosely-coupled federations, in which the member collectives do not submit to potentially coercive forms, can be called confederations. However, this term is old fashioned, potentially confusing and probably unnecessary.