model category, model -category
Definitions
Morphisms
Universal constructions
Refinements
Producing new model structures
Presentation of -categories
Model structures
for -groupoids
on chain complexes/model structure on cosimplicial abelian groups
related by the Dold-Kan correspondence
for equivariant -groupoids
for rational -groupoids
for rational equivariant -groupoids
for -groupoids
for -groups
for -algebras
general -algebras
specific -algebras
for stable/spectrum objects
for -categories
for stable -categories
for -operads
for -categories
for -sheaves / -stacks
(2,1)-quasitopos?
structures in a cohesive (∞,1)-topos
A hypersheaf is a presheaf satisfying descent with respect to all hypercovers.
Hypersheaves are precisely the local objects in the injective or projective local model structure on simplicial presheaves or simplicial sheaves, as originally defined by Joyal and Jardine, i.e. the objects of the hypercompletion of the (∞.1)-topos of (∞,1)-sheaves.
Being a hypersheaf is a stronger property than being an (∞,1)-sheaf. The latter property is also known as Čech descent and the difference between the two was established in Dugger–Hollander–Isaksen.
Last revised on March 23, 2025 at 13:03:51. See the history of this page for a list of all contributions to it.