on chain complexes/model structure on cosimplicial abelian groups
related by the Dold-Kan correspondence
(2,1)-quasitopos?
structures in a cohesive (∞,1)-topos
homotopy theory, (∞,1)-category theory, homotopy type theory
flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed…
models: topological, simplicial, localic, …
see also algebraic topology
Introductions
Definitions
Paths and cylinders
Homotopy groups
Basic facts
Theorems
A model topos is a model category that presents an (∞,1)-topos.
A model category $\mathcal{C}$ is a model topos if there is a simplicial site $K$ and a Quillen equivalence $\mathcal{C} \simeq sPSh(K)_{loc}$ to the local model structure on sSet-presheaves over $K$.
This appears as Rezk, 6.1.
Locally presentable categories: Cocomplete possibly-large categories generated under filtered colimits by small generators under small relations. Equivalently, accessible reflective localizations of free cocompletions. Accessible categories omit the cocompleteness requirement; toposes add the requirement of a left exact localization.
Last revised on July 6, 2018 at 16:25:09. See the history of this page for a list of all contributions to it.