Background
Basic concepts
equivalences in/of -categories
Universal constructions
Local presentation
Theorems
Extra stuff, structure, properties
Models
An (∞,1)-category is sifted if a quasi-category modelling it has the property that
it is not empty,
The diagonal (in sSet) models a cofinal (∞,1)-functor.
Let 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).
The opposite category of the simplex category is a sifted -category.
Every filtered (∞,1)-category is sifted.
In a category of commutative monoids in a symmetric monoidal -category, sifted colimits are computed as sifted colimits in the underlying -category.
See commutative monoid in a symmetric monoidal (∞,1)-category for details.
sifted category, sifted -category
Last revised on September 10, 2021 at 08:53:32. See the history of this page for a list of all contributions to it.