(2,1)-quasitopos?
structures in a cohesive (∞,1)-topos
The notion of -site is the incarnation of the notion of (∞,1)-site when (∞,1)-categories are incarnated as simplicially enriched categories.
An -site is a simplicially enriched category together with the structure of a site on its homotopy category .
This appears as (Toën & Vezzosi 005, def. 3.1.1)
Under the identification of simplicially enriched categories with models for (∞,1)-categories, -sites correspond to (∞,1)-sites.
Because, as discussed at (∞,1)-site, that is equivalently an (∞,1)-category equipped with the structure of a site on its homotopy category of an (∞,1)-category.
For an -site, the local model structure on sSet-presheaves is a presentation of the (∞,1)-topos over the (∞,1)-site corresponding to
model site, simplicial site
Last revised on July 8, 2022 at 17:39:32. See the history of this page for a list of all contributions to it.