Comments on the covariant Sp(2)-symmetric Lagrangian BRST formalism

We give a simple geometrical picture of the basic structures of the covariant Sp(2) symmetric quantization formalism - triplectic quantization - recently suggested by Batalin, Marnelius and Semikhatov. In particular, we show that the appearance of an even Poisson bracket is not a particular property of triplectic quantization. Rather, any solution of the classical master equation generates on a Lagrangian surface of the antibracket an even Poisson bracket. Also other features of triplectic quantization can be identified with aspects of conventional Lagrangian BRST quantization without extended BRST symmetry.