Theorems · Definition · category theory
CategoryTheory.Limits.HasEqualizers
(C : Type u) → [CategoryTheory.Category.{v, u} C] → PropA category HasEqualizers if it has all limits of shape WalkingParallelPair, i.e. if it has
an equalizer for every parallel pair of morphisms.
- Cited by
- 60 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- CategoryTheory.Limits.WalkingParallelPairproof · cited by 781
- CategoryTheory.Limits.HasLimitsOfShapeproof · cited by 223
Cited by68
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.equalizerPullbackMapIsostatement and proof · cited by 10
- CategoryTheory.PreservesImage.isostatement and proof · cited by 9
- CategoryTheory.Limits.image.compIsostatement and proof · cited by 7
- CategoryTheory.Limits.imageSubobjectCompIsostatement and proof · cited by 6
- CategoryTheory.Functor.preservesFiniteLimits_of_preservesHomologyproof · cited by 4
- CategoryTheory.Limits.preservesFiniteLimits_of_preservesEqualizers_and_finiteProductsstatement and proof · cited by 3
- CategoryTheory.Limits.equalizerPullbackMapIso_inv_ι_fststatement and proof · cited by 3
- CategoryTheory.Limits.equalizerPullbackMapIso_inv_ι_sndstatement and proof · cited by 3
- CategoryTheory.ObjectProperty.IsDetecting.isSeparatingstatement and proof · cited by 3
- CategoryTheory.Limits.image.compIso_hom_comp_image_ιstatement and proof · cited by 2
- CategoryTheory.Limits.image.compIso_inv_comp_image_ιstatement and proof · cited by 2
- CategoryTheory.Limits.imageSubobject_iso_compstatement and proof · cited by 2