Theorems · Theorem · category theory
CategoryTheory.Sieve.generate_of_contains_isSplitEpi
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} {R : CategoryTheory.Presieve X} (f : Y ⟶ X)
[CategoryTheory.IsSplitEpi f], R f → CategoryTheory.Sieve.generate R = ⊤If a presieve contains a split epi, it generates the maximal sieve.
- Defined in
- Mathlib.CategoryTheory.Sites.Sieves
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Sievestatement · cited by 552
- CategoryTheory.Presievestatement and proof · cited by 449
- CategoryTheory.Sieve.generatestatement · cited by 117
- CategoryTheory.IsSplitEpistatement and proof · cited by 46
- CategoryTheory.section_proof · cited by 21
- CategoryTheory.IsSplitEpi.idproof · cited by 12
- CategoryTheory.Sieve.id_mem_iff_eq_topproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- CategoryTheory.Sieve.generate_of_singleton_isSplitEpiproof · cited by 2
- CategoryTheory.Sieve.functorPushforward_topproof · cited by 1
- CategoryTheory.Sieve.generate_topproof · cited by 0