Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorDmitri Pavlov
   • CommentTimeFeb 4th 2023
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexCreated: ## Definition A [[site]] is __hypercomplete__ if the [[model structure]] on [[simplicial presheaves]] implementing [[Čech descent]] yields a [[hypercomplete (∞,1)-topos]]. ## Examples * [[Zariski site]], [[Nisnevich site]] * [[Cartesian site]] * [[Stein site]] ## Related concepts * [[Čech descent]], [[hyperdescent]] * [[hypercomplete (∞,1)-topos]] <a href="https://ncatlab.org/nlab/revision/hypercomplete+sites/1">v1</a>, <a href="https://ncatlab.org/nlab/show/hypercomplete+sites">current</a>

   Created:

   Definition

   A site is hypercomplete if the model structure on simplicial presheaves implementing Čech descent yields a hypercomplete (∞,1)-topos.

   Examples

   • Zariski site, Nisnevich site

   • Cartesian site

   • Stein site

   Related concepts

   • Čech descent, hyperdescent

   • hypercomplete (∞,1)-topos

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorDmitri Pavlov
   • CommentTimeFeb 4th 2023
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexRenamed. <a href="https://ncatlab.org/nlab/revision/hypercomplete+site/1">v1</a>, <a href="https://ncatlab.org/nlab/show/hypercomplete+site">current</a>

   Renamed.

   v1, current