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 definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite 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 k-theory lie-theory limits linear linear-algebra locale localization logic mathematics 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.
   • CommentAuthorDavid_Corfield
   • CommentTimeApr 15th 2020
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexI was wondering what this term meant, so thought I'd start this. <a href="https://ncatlab.org/nlab/revision/hypersheaf/1">v1</a>, <a href="https://ncatlab.org/nlab/show/hypersheaf">current</a>

   I was wondering what this term meant, so thought I’d start this.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorDmitri Pavlov
   • CommentTimeMar 23rd 2025
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexAdded: 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. 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](#DHI). ## Related concepts * [[(∞,1)-sheaf]] * [[model structures on simplicial presheaves]] ## References * {#DHI} [[Daniel Dugger]], Sharon Hollander, [[Daniel C. Isaksen]], _Hypercovers and simplicial presheaves_, Mathematical Proceedings of the Cambridge Philosophical Society 136:1 (2004), 9-51. [doi](https://doi.org/10.1017/s0305004103007175), [arXiv](http://arxiv.org/abs/math/0205027). <a href="https://ncatlab.org/nlab/revision/diff/hypersheaf/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/hypersheaf/2">v2</a>, <a href="https://ncatlab.org/nlab/show/hypersheaf">current</a>

   Added:

   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.

   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.

   Related concepts

   • (∞,1)-sheaf

   • model structures on simplicial presheaves

   References

   • {#DHI} Daniel Dugger, Sharon Hollander, Daniel C. Isaksen, Hypercovers and simplicial presheaves, Mathematical Proceedings of the Cambridge Philosophical Society 136:1 (2004), 9-51. doi, arXiv.

   diff, v2, current

3. • CommentRowNumber3.
   • CommentAuthorʇɐ
   • CommentTimeMar 23rd 2025
   • PermaLink
   Author: ʇɐ
   Format: MarkdownItexAdded a quick link to previous pages on [[hypercompletion]]. <a href="https://ncatlab.org/nlab/revision/diff/hypersheaf/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/hypersheaf/3">v3</a>, <a href="https://ncatlab.org/nlab/show/hypersheaf">current</a>

   Added a quick link to previous pages on hypercompletion.

   diff, v3, current