Theorems · Theorem · category theory
CategoryTheory.MorphismProperty.IsLocalAtTarget.mk_of_iff_of_zeroHypercover
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {P : CategoryTheory.MorphismProperty C}
{K : CategoryTheory.Precoverage C} [inst_1 : K.HasPullbacks] [P.RespectsIso],
(∀ {X Y : C} (f : X ⟶ Y) (𝒰 : K.ZeroHypercover Y),
P f ↔ ∀ (i : 𝒰.I₀), P (CategoryTheory.Limits.pullback.snd f (𝒰.f i))) →
P.IsLocalAtTarget K- Cited by
- 4 results in Mathlib
- Foundations
- Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.Limits.pullbackstatement and proof · cited by 864
- CategoryTheory.PreZeroHypercover.I₀statement and proof · cited by 763
- CategoryTheory.PreZeroHypercover.Xstatement and proof · cited by 649
- CategoryTheory.Limits.pullback.sndstatement and proof · cited by 637
- CategoryTheory.PreZeroHypercover.fstatement and proof · cited by 542
- CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercoverstatement and proof · cited by 469
- CategoryTheory.Presieveproof · cited by 449
- CategoryTheory.Limits.HasPullbackproof · cited by 434
- CategoryTheory.PreZeroHypercoverproof · cited by 256
Cited by4
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsZariskiLocalAtTarget.mk'proof · cited by 3
- AlgebraicGeometry.IsZariskiLocalAtSource.isZariskiLocalAtTargetproof · cited by 0
- CategoryTheory.MorphismProperty.IsLocalAtTarget.mk_of_smallproof · cited by 0