Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
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.
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.
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 :-)).
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.
1 to 6 of 6