A sifted $(\infty,1)$-colimit is an (∞,1)-colimit over a diagram that is a sifted (∞,1)-category.
Let $C$ be an (∞,1)-category such that products preserve sifted (∞,1)-colimits (for instance an (∞,1)-topos, see universal colimits).
Then sifted (∞,1)-colimits preserve finite homotopy products.
(simplicial $\infty$-colimits are sifted)
The $(\infty,1)$-colimits of simplicial objects in an $(\infty,1)$-category are sifted.
Simplicial $\infty$-colimits preserve even homotopy fiber products, under mild conditions: see at geometric realization of simplicial topological spaces the section Preservation of homotopy limits.
sifted colimit, sifted $(\infty,1)$-colimit
Last revised on September 21, 2021 at 10:24:54. See the history of this page for a list of all contributions to it.