Theorems · Inductive type · category theory
CategoryTheory.Presieve.HasPullbacks
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] → {X : C} → CategoryTheory.Presieve X → {Y : C} → (Y ⟶ X) → PropA presieve R has pullbacks along f if for every h in R, the pullback
with f exists.
- Defined in
- Mathlib.CategoryTheory.Sites.Sieves
- Cited by
- 9 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.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Presievestatement · cited by 449
Cited by16
Results whose statement or proof uses this declaration.
- CategoryTheory.Presieve.pullbackArrowsstatement · cited by 17
- CategoryTheory.Presieve.pullbackArrows.casesOnstatement and proof · cited by 6
- CategoryTheory.Sieve.pullbackArrows_commstatement and proof · cited by 6
- CategoryTheory.Presieve.HasPullbacks.hasPullbackstatement and proof · cited by 3
- CategoryTheory.Presieve.hasPullbackstatement · cited by 3
- CategoryTheory.Precoverage.hasPullbacks_of_memstatement · cited by 1
- CategoryTheory.Precoverage.HasPullbacks.hasPullbacks_of_memstatement · cited by 1
- CategoryTheory.Precoverage.pullbackArrows_memstatement and proof · cited by 1
- CategoryTheory.Presieve.HasPullbacks.casesOnstatement and proof · cited by 0
- CategoryTheory.Presieve.HasPullbacks.recOnstatement and proof · cited by 0
- CategoryTheory.Presieve.pullbackArrows.congr_simpstatement and proof · cited by 0