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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMar 8th 2012
   • (edited Mar 8th 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added to _[[(infinity,2)-sheaf]]_ a section _[Examples - Codomain fibration / canonical (∞,2)-sheaf](http://ncatlab.org/nlab/show/%28infinity%2C2%29-sheaf#CodomainFibration)_ with the statement that for $\mathcal{X}$ an $(\infty,1)$-topos, the $\infty$-functor $$ A \mapsto \mathcal{X}_{/A} $$ is always an $(\infty,2)$-sheaf with respect to the canonical topology. (It's the $(\infty,2)$-sheaf of "unstable quasicoherent $(\infty,1)$-sheaves"!)

   I have added to (infinity,2)-sheaf a section Examples - Codomain fibration / canonical (∞,2)-sheaf with the statement that for $\mathcal{X}$ an $(\infty,1)$-topos, the $\infty$-functor

   $$A \mapsto \mathcal{X}_{/A}$$

   is always an $(\infty,2)$-sheaf with respect to the canonical topology.

   (It’s the $(\infty,2)$-sheaf of “unstable quasicoherent $(\infty,1)$-sheaves”!)

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeFeb 10th 2016
   • (edited Feb 10th 2016)
   • PermaLink
   Author: Urs
   Format: MarkdownItexChris Kapulking kindly points out to me that somebody has finally written down the "local Joyal model structure" on simplicial presheaves, I have added a pointer here: [Meadows 15](https://ncatlab.org/nlab/show/%28infinity%2C2%29-sheaf#Meadows15)

   Chris Kapulking kindly points out to me that somebody has finally written down the “local Joyal model structure” on simplicial presheaves, I have added a pointer here: Meadows 15