Theorems · Theorem · category theory
TopCat.Presheaf.isSheaf_iff_isSheafUniqueGluing_types
∀ {X : TopCat} (F : TopCat.Presheaf (Type u_4) X), F.IsSheaf ↔ F.IsSheafUniqueGluingFor type-valued presheaves, the sheaf condition in terms of unique gluings is equivalent to the usual sheaf condition.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- CategoryTheory.Functor.objproof · cited by 19,642
- Oppositeproof · cited by 8,081
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.Functor.compproof · cited by 6,529
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- TopCat.carrierproof · cited by 3,184
- iSupproof · cited by 2,415
- TopologicalSpace.Opensproof · cited by 2,040
- TopCatstatement and proof · cited by 1,889
- TypeCat.Funstatement · cited by 1,307
- CategoryTheory.Limits.Cone.ptproof · cited by 1,298
Cited by2
Results whose statement or proof uses this declaration.
- TopCat.Presheaf.isSheaf_of_isSheafUniqueGluing_typesproof · cited by 2
- TopCat.Presheaf.isSheaf_iff_isSheafUniqueGluingproof · cited by 0