nLab
sifted (infinity,1)-colimit

Definition

A sifted $(\mathrm{\infty },1)$-colimit is an (∞,1)-colimit over a diagram that is a sifted (∞,1)-category.

Properties

Proposition

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 products.

This is (Lurie, lemma 5.5.8.11).

Related concepts

• sifted colimit, sifted $(\mathrm{\infty },1)$-colimit

• filtered colimit, filtered (∞,1)-colimit