Theorems · Theorem · category theory
CategoryTheory.Presieve.ofArrows_le_iff
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X : C} {ι : Type u_1} {Y : ι → C} {f : (i : ι) → Y i ⟶ X}
{R : CategoryTheory.Presieve X}, CategoryTheory.Presieve.ofArrows Y f ≤ R ↔ ∀ (i : ι), R (f i)- Defined in
- Mathlib.CategoryTheory.Sites.Sieves
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 25 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.
Cites4
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
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Presievestatement and proof · cited by 449
- CategoryTheory.Presieve.ofArrowsstatement and proof · cited by 150
Cited by10
Results whose statement or proof uses this declaration.
- CategoryTheory.Presieve.pushforward_ofArrowsproof · cited by 2
- CategoryTheory.Presieve.ofArrows_of_uniqueproof · cited by 2
- CategoryTheory.PreZeroHypercover.mem_of_isoproof · cited by 1
- CategoryTheory.Precoverage.ZeroHypercover.Hom.isSheafFor_iffproof · cited by 1
- AlgebraicGeometry.Scheme.Cover.presieve₀_sigmaproof · cited by 1
- CategoryTheory.PreZeroHypercover.Hom.sieve₀_le_sieve₀proof · cited by 1
- CategoryTheory.PreZeroHypercover.presieve₀_restrictIndex_leproof · cited by 0
- CategoryTheory.Presieve.ofArrows_of_isEmptyproof · cited by 0