INJECTIVE POSITIVELY ORDERED MONOIDS .2.

We continue the study of positively ordered monoids (P.O.M.'s). We prove that injective P.O.M.'s are the retracts of the powers of PBAR = [0, infinity]. We also characterize the natural P.O.M.-homomorphism from a given refinement P.O.M. to its bidual, with e.g. applications to decomposition spaces. As another application, we prove that a refinement P.O.M. admits a `Banach limit' if and only if it embeds into a power of PBAR.