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Sep 16, 2015 at 1:56 comment added Peter May I'll get back to this asap. I'm swamped right now. But look at the sketched monomorphism argument using induction, remembering that that is all about primitives. I agree that you have to use the coproduct structure for the statement you question, but logically we don't need it a priori.
Sep 15, 2015 at 21:42 comment added Neil Strickland Thanks, Peter, for your response, but I think I am still not convinced. I have added further explanation to the question.
Sep 14, 2015 at 16:26 history answered Peter May CC BY-SA 3.0