Theorems · Theorem · category theory
CategoryTheory.Limits.eq_of_epi_equalizer
∀ {C : Type u} {X Y : C} [inst : CategoryTheory.Category.{v, u} C] {f g : X ⟶ Y}
[inst_1 : CategoryTheory.Limits.HasEqualizer f g] [CategoryTheory.Epi (CategoryTheory.Limits.equalizer.ι f g)], f = gIf the equalizer of two morphisms is an epimorphism, then the two morphisms are equal.
- Cited by
- 6 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.
Cites8
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.Epistatement and proof · cited by 688
- CategoryTheory.cancel_epiproof · cited by 380
- CategoryTheory.Limits.equalizer.ιstatement and proof · cited by 64
- CategoryTheory.Limits.equalizerstatement · cited by 60
- CategoryTheory.Limits.HasEqualizerstatement and proof · cited by 47
- CategoryTheory.Limits.equalizer.conditionproof · cited by 16
Cited by6
Results whose statement or proof uses this declaration.
- CategoryTheory.PreGaloisCategory.evaluation_injective_of_isConnectedproof · cited by 6
- CategoryTheory.ObjectProperty.IsDetecting.isSeparatingproof · cited by 3
- CategoryTheory.hasInitial_of_isCoseparatingproof · cited by 2
- CategoryTheory.JointlyFaithful.of_jointly_reflects_isIso_of_monoproof · cited by 2
- CategoryTheory.MorphismProperty.eq_of_isomorphisms_descendsAlongproof · cited by 1
- CategoryTheory.eq_of_zeroHypercover_targetproof · cited by 0