Lemma [efr-OH6B]

Let \mathcal {C} be a Markov category. Then \mathcal {C} admits Kolmogorov products of a given cardinality \kappa if and only if \mathcal {C}_\mathrm {det} admits Cartesian products of the same cardinality, and the opfiltered limits of Definition [efr-SIKM] are preserved by the inclusion \mathcal {C}_\mathrm {det} \to \mathcal {C}