Theorems · Definition · category theory
skyscraperSheaf
{X : TopCat} →
(p₀ : ↑X) →
[(U : TopologicalSpace.Opens ↑X) → Decidable (p₀ ∈ U)] →
{C : Type v} →
[inst : CategoryTheory.Category.{u, v} C] → C → [CategoryTheory.Limits.HasTerminal C] → TopCat.Sheaf C XThe skyscraper presheaf supported at p₀ with value A is the sheaf that assigns A to all opens
U that contain p₀ and assigns * otherwise.
- Defined in
- Mathlib.Topology.Sheaves.Skyscraper
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- TopCat.carrierstatement and proof · cited by 3,184
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- TopCatstatement and proof · cited by 1,889
- CategoryTheory.Limits.HasTerminalstatement and proof · cited by 142
- TopCat.Sheafstatement · cited by 73
- skyscraperPresheafproof · cited by 23
- skyscraperPresheaf_isSheafproof · cited by 0
Cited by6
Results whose statement or proof uses this declaration.
- isTerminalSkyscraperSheafObjObjOfNotMemstatement · cited by 1
- isFlasque_skyscraperSheaf_of_epi_fromstatement and proof · cited by 1
- skyscraperSheafFunctorproof · cited by 0
- skyscraperSheaf_obj_mapstatement and proof · cited by 0
- skyscraperSheaf_obj_objstatement and proof · cited by 0
- isFlasque_skyscraperSheaf_of_hasZeroObjectstatement · cited by 0