Theorems · Theorem · category theory
CategoryTheory.Precoverage.pullbackArrows_mem
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Precoverage C} [J.IsStableUnderBaseChange]
{X Y : C} (f : X ⟶ Y) {R : CategoryTheory.Presieve Y},
R ∈ J.coverings Y → ∀ [inst_2 : R.HasPullbacks f], CategoryTheory.Presieve.pullbackArrows f R ∈ J.coverings X- Defined in
- Mathlib.CategoryTheory.Sites.Precoverage
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Limits.pullback.fstproof · cited by 639
- CategoryTheory.Limits.pullback.sndproof · cited by 637
- CategoryTheory.Presievestatement and proof · cited by 449
- CategoryTheory.Limits.HasPullbackproof · cited by 434
- CategoryTheory.Precoveragestatement and proof · cited by 204
- CategoryTheory.Precoverage.coveringsstatement and proof · cited by 194
- CategoryTheory.Presieve.ofArrowsproof · cited by 150
- CategoryTheory.IsPullback.of_hasPullbackproof · cited by 70
- CategoryTheory.IsPullback.flipproof · cited by 61
Cited by1
Results whose statement or proof uses this declaration.