  We present a counterexample showing that Markov categories with conditionals
(such as BorelStoch) need not validate a natural scheme of axioms which we call
contraction identities. These identities hold in every traced monoidal
category, so in particular this shows that BorelStoch cannot be embedded in any
traced monoidal category. We remedy this under the additional assumption of
atomicity: Atomic Markov categories validate all contraction identities, and
furthermore admit a notion of trace defined for non-signalling morphisms. We
conclude that atomic Markov categories admit an intrinsic calculus of combs
without having to assume an embedding into compact-closed categories.
