Injective positively ordered monoids II

International audienceWe continue in this paper the study of positively ordered monoids (POMs) initiated in "Injective positively ordered monoids I". We prove that injective POMs are the retracts of the powers of $[0,\infty ]$. We also characterize the natural POM-homomorphism from a given refinement POM to its bidual, with, for example, applications to decomposition spaces. As another application, we prove that a refinement POM admits a 'Banach limit' if and only if it embeds into a power of $[0,\infty]$