Theorems · Theorem · category theory
TopCat.Presheaf.IsSheaf.isSheafUniqueGluing_types
∀ {X : TopCat} {F : TopCat.Presheaf (Type u_4) X} {ι : Type u_5} {U : ι → TopologicalSpace.Opens ↑X},
F.IsSheaf → ∀ (sf : (i : ι) → F.obj (Opposite.op (U i))), F.IsCompatible U sf → ∃! s, F.IsGluing U sf s- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- Oppositestatement and proof · cited by 8,081
- TopCat.carrierstatement and proof · cited by 3,184
- iSupstatement and proof · cited by 2,415
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- TopCatstatement and proof · cited by 1,889
- TypeCat.Funstatement · cited by 1,307
- Subtype.propproof · cited by 505
- TopCat.Presheafstatement and proof · cited by 371
- ExistsUniquestatement and proof · cited by 268
- CategoryTheory.Functor.mapConeproof · cited by 147
- CategoryTheory.Pairwiseproof · cited by 40
Cited by1
Results whose statement or proof uses this declaration.
- TopCat.Presheaf.IsSheaf.isSheafUniqueGluingproof · cited by 1