Theorems · Theorem · category theory
CategoryTheory.Subfunctor.ofSection_le_iff
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {F : CategoryTheory.Functor Cᵒᵖ (Type w)} {X : Cᵒᵖ}
(x : F.obj X) (G : CategoryTheory.Subfunctor F), CategoryTheory.Subfunctor.ofSection x ≤ G ↔ x ∈ G.obj X- Cited by
- 4 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- 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
- CategoryTheory.Subfunctor.objstatement and proof · cited by 227
- CategoryTheory.Subfunctorstatement and proof · cited by 112
- CategoryTheory.Subfunctor.ofSectionstatement and proof · cited by 14
Cited by4
Results whose statement or proof uses this declaration.
- SSet.Subcomplex.ofSimplex_le_iffproof · cited by 8
- SSet.S.IsUniquelyCodimOneFace.leproof · cited by 2
- CategoryTheory.Subfunctor.ofSection_imageproof · cited by 1
- CategoryTheory.Subfunctor.IsGeneratedBy.memproof · cited by 0