Theorems · Theorem · category theory
CategoryTheory.Sieve.pullback_eq_top_of_mem
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} (S : CategoryTheory.Sieve X) {f : Y ⟶ X},
S.arrows f → CategoryTheory.Sieve.pullback f S = ⊤- Defined in
- Mathlib.CategoryTheory.Sites.Sieves
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Top.topstatement · cited by 9,680
- CategoryTheory.Sievestatement and proof · cited by 552
- CategoryTheory.Sieve.arrowsstatement · cited by 446
- CategoryTheory.Sieve.pullbackstatement · cited by 126
- CategoryTheory.Sieve.mem_iff_pullback_eq_topproof · cited by 7
Cited by5
Results whose statement or proof uses this declaration.
- CategoryTheory.GrothendieckTopology.superset_coveringproof · cited by 37
- CategoryTheory.GrothendieckTopology.intersection_coveringproof · cited by 11
- CategoryTheory.classifier_isSheafproof · cited by 4
- CategoryTheory.GrothendieckTopology.mem_iff_isSheafFor_closedSievesproof · cited by 2
- CategoryTheory.GrothendieckTopology.le_closeproof · cited by 2