The monad formula_42 is thus enough to recover the finitary algebraic category, which allows the following generalization. One says a category is an "algebraic category" if it is monadic over formula_43. This is a more general notion than "finitary algebraic category" because it admits such categories as "CABA" (complete atomic Boolean algebras) and "CSLat" (complete semilattices) whose signatures include infinitary operations. In those two cases the signature is large, meaning that it forms not a set but a proper class, because its operations are of unbounded arity. The algebraic category of sigma algebras also has infinitary operations, but their arity is countable whence its signature is small (forms a set).