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Nov 9, 2011 at 20:18 comment added Benjamin Steinberg You could not identify any identity with 1 and get the universal semi functor to a semigroup.
Nov 9, 2011 at 12:21 comment added user2529 Should every identity arrow be made equivalent to 1? Perhaps a pointed version is better, and only the identity arrow of the point be made equivalent to 1.
Nov 9, 2011 at 11:59 vote accept CommunityBot
Nov 9, 2011 at 11:55 comment added user2529 Ah, oh so there is a group version and a monoid version. Indeed universal monoid is a good name for it. Thanks. This is indeed what I was looking for.
Nov 6, 2011 at 22:24 comment added Martin Brandenburg Ah, this seems to fit to the question.
Nov 6, 2011 at 16:30 history answered Benjamin Steinberg CC BY-SA 3.0