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We construct and compare two alternative quantizations, as a time-orderableprefactorization algebra and as an algebraic quantum field theory valued incochain complexes, of a natural collection of free BV theories on the categoryof $m$-dimensional globally hyperbolic Lorentzian manifolds. Our comparison isrealized as an explicit isomorphism of time-orderable prefactorizationalgebras. The key ingredients of our approach are the retarded and advancedGreen's homotopies associated with free BV theories, which generalize retardedand advanced Green's operators to cochain complexes of linear differentialoperators.

Quantization of Lorentzian free BV theories: factorization algebra vs algebraic quantum field theory