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Strictly speaking, electric current is a concept in physics. It is defined as the "flow of electric charges in a unit time". The "charges" referred to in the definition do not limited to electron, it includes all types of charges, e.g. protons, positrons, +ve ions, -ve ions .....
The direction of current is further defined as the direction of flow of positive charges. Hence, a beam of protons flowing to the right constitutes an electric current flowing to the right.
Since electrons carries -ve charges, a beam of electrons flowing to the right can be construed (or imagined) as physically equivalent to a beam of positive charges of the same (charge) magnitude flowing to the left.