Theorem [efr-FTTL]

Let \kappa be a regular cardinal. Let \mathsf {Set}_{\bar {\Delta }}^{< \kappa } denote the subcategory of \mathsf {Set}_{\bar {\Delta }} consisting of the sets of cardinality less than \kappa . Then \mathsf {Set}_{\bar {\Delta }}^{< \kappa } is the initial \kappa -distributive, externally iterable, coinflip Markov category. In particular, \mathsf {FinStoch} is the initial distributive, externally iterable, coinflip Markov category, and \mathsf {Set}_{\bar {\Delta }} is the initial small-distributive, externally iterable, coinflip Markov category.