The problem of obtaining the necessary and sufficient conditions, which ensure the consistency, completeness and relativistic covariance of the system of equal-time commutators has been stated and solved. The difficulties arise from the fact that the system of the commutators is cumbersome and put down in a noncovariant form. These difficulties have been tackled by the functorial transition from the category of quantum fields into the category of universal algebras. In the universal algebra each local quantity is represented by the corresponding element of the algebra. The elements of the algebra have no coordinate dependence. Each equal-time commutator is represented by the finite set of various nonassociative multiplications. The energy stress tensor has to be included into the system of commutators for deriving the relativistic invariance conditions.