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one more remark at relation between quasi-categories and simplicial categories
(to be expanded...)
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.
Thanks for the alert. Could you fix it?
Thanks!
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.
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).
so let’s add the publication data proper:
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