Definition
U20: “there should be some transport map that at least gets to within some eps”. A50: “There is no requirement that the transport be invertible or symmetric … transporting the communicative structure of a nineteenth-century poem into contemporary slang need not be equivalent to transporting the modern version back.” A50 §6 made translation itself a stochastic reconstruction kernel T(v | u, c), not a map u ↦ v; A52 §4.1 called these “stochastic transport kernels”.
What it is not
Not a correspondence witnessing equivalence, which is what Φ was from A34 to A49. Manuscript §6: “A transport from source C_o to target C_t consists of a correspondence τ between appropriate source and target contexts and local stochastic kernels … It is intentionally directed: compression and interpretation need not be invertible.” That definition arrived at A81 §5.2: K_C : E_o(C) ⇝ E_t(τ(C)), “Require appropriate compatibility with restriction maps when a transport is intended to preserve observational structure. Formulate the resulting construction as a morphism or lax morphism between observational systems.” C6 Appendix B: “restrict_tau(D) K_C = K_D restrict_D, interpreted as equality of kernels. This naturality-like law means that transporting and forgetting observations agrees with forgetting and transporting.” The lax-morphism framing, which would have named the approximate case categorically, did not reach C6 or the manuscript. A86 also modelled translation as an utterance-level channel T(v | u); the two levels are never formally related, and the manuscript uses both.