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1. • CommentRowNumber1.
   • CommentAuthorTim_Porter
   • CommentTimeFeb 21st 2012
   • (edited Feb 21st 2012)
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexI was looking for the simplest (explicit) proof that a quasi-category is a (infinity,1)-category, i.e. that 2-cells and above are equivalences. All of our entries more or less assume this rather than indicating a proof, so then I looked but could not find an explicit reference, in the nLab pages, to a proof in the literature. What is the best source for that?

   I was looking for the simplest (explicit) proof that a quasi-category is a (infinity,1)-category, i.e. that 2-cells and above are equivalences. All of our entries more or less assume this rather than indicating a proof, so then I looked but could not find an explicit reference, in the nLab pages, to a proof in the literature. What is the best source for that?

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeFeb 21st 2012
   • (edited Feb 21st 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItexIt's the same proof as for Kan complexes: exhibiting the inverse of a 2-cell only needs filling inner horns.

   It’s the same proof as for Kan complexes: exhibiting the inverse of a 2-cell only needs filling inner horns.

3. • CommentRowNumber3.
   • CommentAuthorTim_Porter
   • CommentTimeFeb 21st 2012
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexI knew it for 2-cells (and so can manufacture a proof in higher dimensions). I was partially pointing out that even this seems not to be given in a prominent position in 'the literature'. I looked for it in both Joyal's notes and in Lurie, (not a thorough search in either case) and could not find it. It also relates to the query that is still there at the foot of [[quasi-category]].

   I knew it for 2-cells (and so can manufacture a proof in higher dimensions). I was partially pointing out that even this seems not to be given in a prominent position in ’the literature’. I looked for it in both Joyal’s notes and in Lurie, (not a thorough search in either case) and could not find it. It also relates to the query that is still there at the foot of quasi-category.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeFeb 21st 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexHi Tim, in Lurie's book this is discussed in section 1.2.2 "Mapping spaces in higher category theory". Proposition 1.2.2.3 there is the statement that you are after.

   Hi Tim,

   in Lurie’s book this is discussed in section 1.2.2 “Mapping spaces in higher category theory”. Proposition 1.2.2.3 there is the statement that you are after.

5. • CommentRowNumber5.
   • CommentAuthorTim_Porter
   • CommentTimeFeb 21st 2012
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexThanks that is a great help.

   Thanks that is a great help.