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I have touched the section “As Kan complexes” (here), slightly expanding text and cross-linking.
In particular, I have
cross-linked with the illustrative examples of 1-(hyper-)groupoids (here)
provided a link for the statement that every -type is modeled by a 2-coskeletal Kan complex.
What is missing is a statement/pointer about reflecting all the way down to -hypergroupoids
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