so let’s add the publication data proper:

- Emily Riehl,
*On the structure of simplicial categories associated to quasi-categories*, Math. Proc. Camb. Phil. Soc.**150**(2011) 489-504 [arXiv:0912.4809, doi:10.1017/S0305004111000053]

Fixed a defunct link.

]]>In particular, it used to say in the references section that the Quillen equivalence “is described in” Bergner (2007), while Lurie (2009) was only found at the end of the list. I have changed that.

]]>touched wording and formatting, added publication data to references.

Finally hyperlinked the previously unnamed operation $\mathfrak{C}$ of *rigidification of quasi-categories* (entry to be created now).

Lightened the wording slightly.

]]>Somehow, I had completely missed the homotopy coherent nerve page had much of what I wrote (albeit with the opposite ordering convention on homspaces). So I’ve removed the additions, and will probably add in the additional examples over there.

]]>I wanted to add the reason I chose the ordering convention I did on the hom-sets is by analogy with lax operations that have the direction $[g] \cdot [f] \to [gf]$.

Also, this has analogy with the Duskin nerve, and it is the ordering used in Lurie’s Kerodon, 2.4.3.1 (simplicial path categories), which later uses this when discussing $(\infty,2)$-categories.

]]>Added in the calculation of $\mathfrak{C}$ for some nice simplicial sets.

]]>R is fibrant replacement for the Dwyer-Kan-Bergner model structure, not the Joyal one.

]]>Best,

Viktoriya ]]>

Thanks!

]]>Added more details and references. Changed the notation to the one used in Bergner’s book.

]]>added the qualifiers “derived” and “fibrant”, which were probably missing.

But this entry still needs to cite actual facts anyways, where it currently says

]]>(…details/links…)

Thanks for the alert. Could you fix it?

]]>This claim was added by Urs in Revision 7 on February 11, 2010.

I am pretty sure that the homotopy coherent nerve functor must be derived, since it doesn’t preserve weak equivalence of arbitrary simplicial categories.

]]>I am aware that this entry is quite old and not finished. However, I was wondering if it is a typo or a theorem (and in the latter case, I would be interested in a reference) that in the relation via the homotopy coherent nerve, neither the simplicial category C is assumed to be fibrant nor the unit is derived. I would be curious about any sort of insight here.

Best,

Viktoriya Ozornova ]]>

one more remark at relation between quasi-categories and simplicial categories

(to be expanded...)

]]>