Abstract
Introduction. We give necessary and sufficient conditions for the monicity of any given unit morphism associated with an algebraic functor and its left adjoint. The direct verification of these conditions in specific cases can be somewhat subtle. However, a stronger set of sufficient conditions for monicity may be given which is easier to check directly. The latter conditions are still sufficiently general to provide a categorical form for the proof of the Birkhoff Witt theorem, closely related to Birkhoff's original proof [3], as well as one for the Schreier theorem on free products of groups with amalgamated subgroups [1], [5].
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