Theorems · Theorem · category theory
CategoryTheory.Subfunctor.family_of_elements_compatible
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {F : CategoryTheory.Functor Cᵒᵖ (Type w)}
(G : CategoryTheory.Subfunctor F) {U : Cᵒᵖ} (s : F.obj U), (G.familyOfElementsOfSection s).Compatible- Defined in
- Mathlib.CategoryTheory.Subfunctor.Sieves
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- Opposite.unopstatement and proof · cited by 2,231
- Quiver.Hom.opproof · cited by 1,948
- CategoryTheory.Functor.map_compproof · cited by 734
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.Subfunctor.to_sheafifyLiftproof · cited by 1
- CategoryTheory.Subfunctor.eq_sheafifyproof · cited by 1