Theorems · Theorem · category theory
CategoryTheory.Presieve.hasPullback
∀ {C : Type u₁} {inst : CategoryTheory.Category.{v₁, u₁} C} {X : C} {R : CategoryTheory.Presieve X} {Y : C} (f : Y ⟶ X)
[self : R.HasPullbacks f] {Z : C} {h : Z ⟶ X}, R h → CategoryTheory.Limits.HasPullback h fAlias of CategoryTheory.Presieve.HasPullbacks.hasPullback.
- Defined in
- Mathlib.CategoryTheory.Sites.Sieves
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- CategoryTheory.Limits.HasPullbackstatement · cited by 434
- CategoryTheory.Presieve.HasPullbacksstatement · cited by 9
- CategoryTheory.Presieve.HasPullbacks.hasPullbackproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- CategoryTheory.Sieve.pullbackArrows_commproof · cited by 6
- CategoryTheory.Presieve.pullbackArrows.casesOnstatement · cited by 6
- CategoryTheory.Precoverage.pullbackArrows_memproof · cited by 1
- CategoryTheory.Presieve.pullbackArrows.recOnstatement · cited by 0
- CategoryTheory.Presieve.FactorsThruAlong.pullbackArrowsproof · cited by 0