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Created reflexive coequalizer.
Somebody asks me by email where the proofs for the claims at reflexive coequalizers can be found. Apparently not all of them are in the single reference cited there, and the question is to who to attribute them. But I haven’t checked, no time right now. Somebody who feels responsible for this please check. (I suggested to that person to forward his question to here, but I don’t know if he will.)
Urs, I think there are other entries which indicate the proofs, but I’m happy to give them here as well (at least some of them). Linton was of course cited.
Edit: I recall that a proof of proposition 1 is given on page 1 of Johnstone’s Topos Theory (baby elephant), at least in essence. But somebody who has that book at hand can hopefully confirm.
I understand the question as mainly asking for who to attribute these statements to, as some of them are apparently not in Linton. I haven’t checked. But if you can add a remark clarifying this, it would be great in any case.
Well, I’ve added a proof of proposition 1 and some other things, and I cited things as best as I have direct knowledge of. Some of this might be folkloric; I’d maybe take a peek at the Johnstone reference, but I don’t think he cited a source for the lemma on page 1. Some of this reprises material in colimits in categories of algebras.
Thanks, Todd! That’s awesome. I’ll notify my correspondent of these additions (in case he didn’t follow my pointer to have a look here at the forum…)
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