Corollary [efr-ILIQ]

The free Markov prefibration monad \overline {(-)}|_\mathrm {det} commutes with fiberwise opposites. In particular, algebra structures on \mathcal {D}_0 are in bijection with algebra structures on \mathcal {D}_0^\mathrm {fop}, and fiberwise opposites lifts to an involution of \mathsf {Alg}(\overline {(-)}|_\mathrm {det}).