The free category on the 1-vertex 1-edge graph is just the monoid (N,+,0) of natural numbers. Although it was somewhat fashionable in the 19th century to distinguish actual existence of numbers from the potential existence of the set of all numbers, the actual-potential distinction has since faded in importance for most constructivists. A more modern constructive concern would be with the existence of a well-ordering of the continuum. That aside, the odds are good that anyone who did not recognize the existence of the natural numbers is likely to doubt that you could produce a graph having an infinite number of nodes. If you're prepared to produce the latter, why would it bother you to have someone produce the former? Vaughan Pratt ----------- Galchin Vasili wrote:
Hello,
Let G be a directed graph that either has an infinite # of nodes or has edges which are loops.
Would a constructist recognize the existence of G's free category?
Thank you, Bill Halchin