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Apr 4 at 5:14 comment added Kevin Carlson @NikolaTomić Well, the nLab discusses Hopf monoids, but that is not what you've written about.
Apr 3 at 17:06 comment added Nikola Tomić I thought it was the general definition of cogroup no ? In the nlab page they talk about group object in general monoidal category so I thought it made sense to talk about cogroup in that setting. Moreover, Hopf algebras fits in that setting, so I didn't feel I was saying something new. I've elaborated because I found the nlab page a bit unclear about it ("A cogroup is a group in C^op" (which C^op ?)) + I wanted to add some examples.
Apr 3 at 16:56 comment added Vladimir Dotsenko Just the fact that you think that some new definition is better than the existing one is not quite a sufficient reason to arbitrarily redefine existing notions, no? I think the question was "what is a cogroup", rather than "how would you like to redefine the notion of a cogroup"...
Apr 3 at 15:34 history edited Kevin Casto CC BY-SA 4.0
Fixed hyphens in last par
Apr 3 at 13:29 history edited Nikola Tomić CC BY-SA 4.0
added 338 characters in body
Apr 3 at 13:23 comment added Nikola Tomić Oh yes you're right, thanks I have edited the answer.
Apr 3 at 13:23 history edited Nikola Tomić CC BY-SA 4.0
added 338 characters in body
Apr 3 at 13:19 vote accept CommunityBot
Apr 3 at 13:19
Apr 3 at 13:02 comment added David Roberts To get a group object in a monoidal category you need diagonals, so you can express the inverse axiom. So to get a cogroup object in a monoidal category, you need codiagonals.
Apr 3 at 12:52 history answered Nikola Tomić CC BY-SA 4.0