Theorems · Definition · category theory
CategoryTheory.Sieve.equalizer
{C : Type uC} → [inst : CategoryTheory.Category.{vC, uC} C] → {U V : C} → (U ⟶ V) → (U ⟶ V) → CategoryTheory.Sieve UFor two arrows f₁ f₂ : U ⟶ V, the arrows i such that i ≫ f₁ = i ≫ f₂ forms a sieve.
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses propext
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Sievestatement · cited by 552
Cited by12
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.coverPreserving_restrictedTopologyproof · cited by 3
- CategoryTheory.Functor.functorPushforward_equalizer_memstatement · cited by 3
- CategoryTheory.Functor.IsDenseSubsite.equalizer_memstatement · cited by 2
- CategoryTheory.Functor.IsLocallyFaithful.extproof · cited by 1
- CategoryTheory.Functor.IsLocallyFaithful.functorPushforward_equalizer_memstatement · cited by 1
- CategoryTheory.Sieve.equalizer_applystatement and proof · cited by 1
- CategoryTheory.Functor.IsDenseSubsite.map_eq_of_eqproof · cited by 1
- CategoryTheory.Functor.IsLocallyFaithful.casesOnstatement and proof · cited by 0
- CategoryTheory.Functor.IsLocallyFaithful.recOnstatement and proof · cited by 0
- CategoryTheory.Sieve.equalizer_eq_equalizerSievestatement · cited by 0
- CategoryTheory.Sieve.equalizer_selfstatement · cited by 0