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• CommentRowNumber1.
• CommentAuthorAlec Rhea
• CommentTimeMar 2nd 2021

Test edit, I can’t seem to get the page to accept the larger edit I’ve made.

• CommentRowNumber2.
• CommentAuthorAlec Rhea
• CommentTimeMar 2nd 2021

Added discussion of skeletons as an endo-2-functor on the 2-category of categories, skeletons of indexed categories and skeletons of fibrations. There is probably a more general discussion to be had at the $\infty$-level, but I’m not sure what $\infty$-skeleta look like at the moment.

• CommentRowNumber3.
• CommentAuthorHurkyl
• CommentTimeMar 2nd 2021
• (edited Mar 2nd 2021)

In the case of quasi-categories, I imagine Lurie’s “minimal inner fibrations” (Higher Topos Theory, 2.3.3) would be the right notion of ∞-skeleton to consider.

I guess then the right thing for simplicial categories is to combine the evident condition on objects with requiring the hom-spaces be minimal Kan fibrations.

1. Apologies that you had to battle the spam filter Alec, it is suspicious of large edits (but becomes less suspicious the more of an editing history one has, until it eventually allow one free reign :-)).

• CommentRowNumber5.
• CommentAuthorAlec Rhea
• CommentTimeMar 3rd 2021

Slightly changed definition section to explicitly name skeletons vs weak skeletons, and added a simple theorem about the stronger sense of skeletons without without choice.

The changes to the definition section might be controversial, as I named the weaker version a ’weak skeleton’ and defined a skeleton to be the classical notion. If there is more standard terminology it should be put in this section.

• CommentRowNumber6.
• CommentAuthorAlec Rhea
• CommentTimeMar 7th 2021

Added coherence isomorphisms for skeleton endo-pseudofunctor.