Theorems · Theorem · category theory
CategoryTheory.Limits.equalizer.condition
∀ {C : Type u} {X Y : C} [inst : CategoryTheory.Category.{v, u} C] (f g : X ⟶ Y)
[inst_1 : CategoryTheory.Limits.HasEqualizer f g],
CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.equalizer.ι f g) f =
CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.equalizer.ι f g) g- Cited by
- 16 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.compstatement · cited by 17,999
- CategoryTheory.Limits.parallelPairproof · cited by 766
- CategoryTheory.Limits.limit.coneproof · cited by 97
- CategoryTheory.Limits.equalizer.ιstatement · cited by 64
- CategoryTheory.Limits.equalizerstatement · cited by 60
- CategoryTheory.Limits.HasEqualizerstatement and proof · cited by 47
- CategoryTheory.Limits.Fork.conditionproof · cited by 11
Cited by19
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.eq_of_epi_equalizerproof · cited by 6
- CategoryTheory.Limits.image.extproof · cited by 4
- CategoryTheory.Limits.equalizerIsEqualizerstatement · cited by 4
- AlgebraicGeometry.ext_of_isDominant_of_isSeparatedproof · cited by 3
- CategoryTheory.Limits.equalizerSubobject_arrow_compproof · cited by 3
- CategoryTheory.Limits.preservesLimit_of_preservesEqualizers_and_productproof · cited by 2
- CategoryTheory.Preadditive.hasEqualizer_of_hasKernelproof · cited by 2
- CategoryTheory.NormalMonoCategory.epi_of_zero_cokernelproof · cited by 2
- CategoryTheory.JointlyFaithful.of_jointly_reflects_isIso_of_monoproof · cited by 2
- AlgebraicGeometry.ext_of_fromSpecResidueField_eqproof · cited by 1
- CategoryTheory.hasInitial_of_weakly_initial_and_hasWideEqualizersproof · cited by 0