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The old entry 1-groupoid was a bit vague. I have added a paragraph with a more precise description.
I have just been looking at 1-hypergroupoids as a prelude to talking about n-hypergroupoids (in the sense of Duskin, but also Glenn) in some work for the Profinite monograph. How might that topic and terminology be best melded in with this (and related) entries?
Hi Tim,
not sure what you are asking. There is a quick note at n-groupoid – As Kan complexes.
What is missing on the $n$Lab, it seems, is the discussion of how $n$-hypergroupoids exhaust $(n+1)$-cosketal Kan complexes up to equivalence.
There is a neat version of (probably) Glenn’s version of n-hypergroupoids in Munoz’s thesis. (This uses a truncted simp. object then has a specific lift, an n-bracket, that is a bit like algebraic Kan conditions. I have not completely worked out what to do with them, but they give the structure (with 4 axioms). I have mislaid Glenn’s paper so cannot check if that stuff was in there. There is good stuff in Beke’s paper, but the links are not all that I would want. I will try to put some more stuff up on the hypergroupoid entry, when I have worked things through a it more.
I like the account of $n$-hypergroupoids in Pridham 09.
Yes. That is a good one.
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