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am starting fibrations of quasi-categories
oh, darn we already had fibrations of simplicial sets
will merge that...
I left fibrations of quasi-categories and made fibrations of simplicial sets redirect to that.
That's not entirely consistent terminology, but the other way round it seemed to be worse to me, because tomorrow somebody will come up with a model of (oo,n)-categories on simplicial sets and introduce a plethora of new notions of fibrations. So it is important to state the context in the title, i'd think.
I am expanding fibrations of quasi-categories. So far mainly a list of properties of left/right fibrations.
discovered that we have this entry
changed page name to singular
added missing redirects, such as for fibered (∞,1)-category
added missing cross-links, with
added pointer to:
While it’s unclear what was meant by “higher categorical meaning” – there is (IIRC) a model structure on marked simplicial sets presenting the $(\infty,1)$-category of relative $(\infty,1)$-categories (i.e. the subcategory of $(\infty,1)Cat^{[1]}$ spanned by essentially surjective monomorphisms). Even if I’m misremembering, there is a simplicially-enriched subcategory that presents that $(\infty,1)$-category. (quasicategories with ’semisaturated’ markings, generalizing semisaturated relative categories)
So there is some genuinely interesting higher categorical content in the comparison with the marked model structure.
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