Remark [efr-A7K7]

The pullbacks appearing in Definition [efr-T3HM] are of course pullbacks in \mathcal {C}_\mathrm {det}, not \mathcal {C}, analogously to how X \otimes Y is a product in \mathcal {C}_\mathrm {det}, not \mathcal {C}. We will still use the notation X \times _Z Y for these pullbacks, which should not lead to any confusion. We may occasionally write X \times Y instead of X \otimes Y, if we are carrying out a construction which primarily involves \mathcal {C}_\mathrm {det}. Since essentially no Markov categories have Cartesian products (except when the tensor product is Cartesian), this should also not lead to any ambiguity.