Theorems · Definition · category theory
CategoryTheory.Limits.equalizerIsEqualizer
{C : Type u} →
{X Y : C} →
[inst : CategoryTheory.Category.{v, u} C] →
(f g : X ⟶ Y) →
[inst_1 : CategoryTheory.Limits.HasEqualizer f g] →
CategoryTheory.Limits.IsLimit (CategoryTheory.Limits.Fork.ofι (CategoryTheory.Limits.equalizer.ι f g) ⋯)The equalizer built from equalizer.ι f g is limiting.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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.Limits.Cone.ptproof · cited by 1,298
- CategoryTheory.Limits.WalkingParallelPairstatement · cited by 781
- CategoryTheory.Limits.parallelPairstatement and proof · cited by 766
- CategoryTheory.Iso.reflproof · cited by 727
- CategoryTheory.Limits.IsLimitstatement · cited by 664
- CategoryTheory.Limits.limit.isLimitproof · cited by 146
- CategoryTheory.Limits.limit.coneproof · cited by 97
- CategoryTheory.Limits.Fork.ofιstatement · cited by 66
- CategoryTheory.Limits.equalizer.ιstatement · cited by 64
- CategoryTheory.Limits.equalizerstatement · cited by 60
Cited by5
Results whose statement or proof uses this declaration.
- CategoryTheory.JointlyFaithful.of_jointly_reflects_isIso_of_monoproof · cited by 2
- CategoryTheory.Limits.preservesLimit_of_preservesEqualizers_and_productproof · cited by 2
- CategoryTheory.Preadditive.hasEqualizer_of_hasKernelproof · cited by 2
- CategoryTheory.Limits.isLimitOfHasEqualizerOfPreservesLimitproof · cited by 0
- CategoryTheory.Limits.PreservesEqualizer.of_iso_comparisonproof · cited by 0