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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeFeb 11th 2010
   • PermaLink
   Author: Urs
   Format: Markdownam starting [[fibrations of quasi-categories]]

   am starting fibrations of quasi-categories

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeFeb 11th 2010
   • (edited Feb 11th 2010)
   • PermaLink
   Author: Urs
   Format: Markdownoh, darn we already had [[fibrations of simplicial sets]] will merge that...

   oh, darn we already had fibrations of simplicial sets

   will merge that...

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeFeb 11th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownI 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 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.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeFeb 17th 2010
   • (edited Feb 17th 2010)
   • PermaLink
   Author: Urs
   Format: MarkdownI am expanding [[fibrations of quasi-categories]]. So far mainly a list of properties of left/right fibrations.

   I am expanding fibrations of quasi-categories. So far mainly a list of properties of left/right fibrations.

5. • CommentRowNumber5.
   • CommentAuthorTim_Porter
   • CommentTimeOct 5th 2019
   • (edited Oct 5th 2019)
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexChanged 'fib rations' to 'fibrations'! <a href="https://ncatlab.org/nlab/revision/diff/fibrations+of+quasi-categories/23">diff</a>, <a href="https://ncatlab.org/nlab/revision/fibrations+of+quasi-categories/23">v23</a>, <a href="https://ncatlab.org/nlab/show/fibrations+of+quasi-categories">current</a>

   Changed ’fib rations’ to ’fibrations’!

   diff, v23, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeAug 26th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexdiscovered that we have this entry changed page name to singular added missing redirects, such as for `fibered (∞,1)-category` added missing cross-links, with * [[fibered category]] * [[n-fibration|$n$-fibration]] * [[universal fibration of (∞,1)-categories]] added pointer to: * [[Ulrik Buchholtz]], [[Jonathan Weinberger]], *Synthetic fibered (∞,1)-category theory* &lbrack;[arXiv:2105.01724](https://arxiv.org/abs/2105.01724)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/fibration+of+quasi-categories/25">diff</a>, <a href="https://ncatlab.org/nlab/revision/fibration+of+quasi-categories/25">v25</a>, <a href="https://ncatlab.org/nlab/show/fibration+of+quasi-categories">current</a>

   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

   • fibered category

   • $n$-fibration

   • universal fibration of (∞,1)-categories

   added pointer to:

   • Ulrik Buchholtz, Jonathan Weinberger, Synthetic fibered (∞,1)-category theory [arXiv:2105.01724]

   diff, v25, current

7. • CommentRowNumber7.
   • CommentAuthorDmitri Pavlov
   • CommentTimeOct 26th 2023
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexRedirect: Joyal fibration. <a href="https://ncatlab.org/nlab/revision/diff/fibration+of+quasi-categories/26">diff</a>, <a href="https://ncatlab.org/nlab/revision/fibration+of+quasi-categories/26">v26</a>, <a href="https://ncatlab.org/nlab/show/fibration+of+quasi-categories">current</a>

   Redirect: Joyal fibration.

   diff, v26, current

8. • CommentRowNumber8.
   • CommentAuthorChristian Sattler
   • CommentTimeAug 6th 2024
   • PermaLink
   Author: Christian Sattler
   Format: MarkdownItexDelete a wrong remark. The fibrations in the marked model structure also have no intrinsic higher categorical meaning. <a href="https://ncatlab.org/nlab/revision/diff/fibration+of+quasi-categories/27">diff</a>, <a href="https://ncatlab.org/nlab/revision/fibration+of+quasi-categories/27">v27</a>, <a href="https://ncatlab.org/nlab/show/fibration+of+quasi-categories">current</a>

   Delete a wrong remark. The fibrations in the marked model structure also have no intrinsic higher categorical meaning.

   diff, v27, current

9. • CommentRowNumber9.
   • CommentAuthorHurkyl
   • CommentTimeAug 6th 2024
   • PermaLink
   Author: Hurkyl
   Format: MarkdownItexWhile 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.

   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.