There are evident similarities between Clifford, Weil and Universal Enveloping algebras. Each may be defined directly as a quotient of the tensor algebra $T(V)$ divided by an ideal generated by some algebraic relations and for each of those there is an alternative definition given by universal property.
Are these algebras generalize to some more general objects (algebraic or categorical ones) and were they been studied? As a side note, these types of algebras resembles coordinate rings on algebraic varieties. Did anyone compared those categories in any way?