Theorems · Inductive type · category theory
CategoryTheory.Presieve.HasPairwisePullbacks
{C : Type u₁} → [inst : CategoryTheory.Category.{v₁, u₁} C] → {X : C} → CategoryTheory.Presieve X → PropGiven a presieve R on X, the predicate R.HasPairwisePullbacks means that for all arrows
f and g in R, the pullback of f and g exists.
- Defined in
- Mathlib.CategoryTheory.Sites.Sieves
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.Presievestatement · cited by 449
Cited by35
Results whose statement or proof uses this declaration.
- CategoryTheory.Equalizer.Presieve.Arrows.SecondObjstatement and proof · cited by 7
- CategoryTheory.Equalizer.Presieve.Arrows.firstMapstatement and proof · cited by 6
- CategoryTheory.Equalizer.Presieve.Arrows.secondMapstatement and proof · cited by 6
- CategoryTheory.Presieve.Arrows.PullbackCompatiblestatement and proof · cited by 5
- CategoryTheory.Equalizer.Presieve.Arrows.SecondObj.extstatement and proof · cited by 3
- CategoryTheory.Presieve.HasPairwisePullbacks.has_pullbacksstatement and proof · cited by 3
- CategoryTheory.Equalizer.Presieve.SecondObjstatement and proof · cited by 3
- CategoryTheory.Equalizer.Presieve.firstMapstatement and proof · cited by 3
- CategoryTheory.Equalizer.Presieve.secondMapstatement and proof · cited by 3
- CategoryTheory.Presieve.FamilyOfElements.PullbackCompatiblestatement and proof · cited by 2
- CategoryTheory.Presieve.preservesProduct_of_isSheafForstatement and proof · cited by 2
- CategoryTheory.Equalizer.Presieve.wstatement and proof · cited by 2