A great question ... and I do not have an answer for it. However, regarding P (<) Q as a (posetal) module between the posets it does have the striking property that it is the final module! -robin ________________________________ From: Dana Scott <scott@cs.cmu.edu> Sent: Sunday, August 13, 2017 1:55:11 PM To: categories@mta.ca Subject: categories: An elementary question The category of posets (= partially ordered sets) and monotone maps is often used as an easy example -- different from the category of sets -- that has products, coproducts, and is cartesian closed but not a topos. Let P and Q be two posets. Define (P (<) Q) as the modified coproduct where all the elements of P are made less than all the elements of Q. QUESTION. Does (P (<) Q) have a nice categorical definition as a functor in the category of posets? [For admin and other information see: http://www.mta.ca/~cat-dist/ ]