Theorems · Definition · category theory
CategoryTheory.Limits.HasEqualizer
{C : Type u} → {X Y : C} → [inst : CategoryTheory.Category.{v, u} C] → (X ⟶ Y) → (X ⟶ Y) → PropTwo parallel morphisms f and g have an equalizer if the diagram parallelPair f g has a
limit.
- Cited by
- 47 results in Mathlib
- Foundations
- Depth 19 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.Limits.parallelPairproof · cited by 766
- CategoryTheory.Limits.HasLimitproof · cited by 226
Cited by69
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.equalizer.ιstatement and proof · cited by 64
- CategoryTheory.Limits.equalizerstatement and proof · cited by 60
- CategoryTheory.Limits.equalizer.hom_extstatement and proof · cited by 27
- CategoryTheory.Limits.equalizer.liftstatement and proof · cited by 19
- CategoryTheory.Limits.equalizer.conditionstatement and proof · cited by 16
- CategoryTheory.Limits.equalizerSubobjectstatement and proof · cited by 10
- CategoryTheory.Limits.eq_of_epi_equalizerstatement and proof · cited by 6
- CategoryTheory.Limits.equalizerComparisonstatement and proof · cited by 6
- CategoryTheory.Limits.equalizerSubobjectIsostatement and proof · cited by 5
- CategoryTheory.Comonad.ComonadicityInternal.comparisonAdjunctionstatement and proof · cited by 4
- CategoryTheory.Comonad.ComonadicityInternal.comparisonRightAdjointHomEquivstatement and proof · cited by 4
- CategoryTheory.Comonad.ComonadicityInternal.comparisonRightAdjointObjstatement and proof · cited by 4