Theorems · Definition · category theory
CategoryTheory.Limits.HasWeakEqualizer
{C : Type u_1} → [inst : CategoryTheory.Category.{v_1, u_1} C] → {X Y : C} → (X ⟶ Y) → (X ⟶ Y) → PropTwo parallel morphisms f and g have a weak equalizer if the diagram parallelPair f g
has a weak limit.
- Cited by
- 10 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.HasWeakLimitproof · cited by 17
Cited by16
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.weakEqualizer.ιstatement and proof · cited by 9
- CategoryTheory.Limits.weakEqualizerstatement and proof · cited by 7
- CategoryTheory.Limits.weakEqualizer.liftstatement and proof · cited by 4
- CategoryTheory.Limits.weakEqualizer.conditionstatement and proof · cited by 3
- CategoryTheory.Limits.weakEqualizer.forkstatement and proof · cited by 3
- CategoryTheory.Preadditive.hasWeakEqualizer_of_hasWeakKernelstatement · cited by 1
- CategoryTheory.Limits.weakEqualizer.lift_ιstatement and proof · cited by 1
- CategoryTheory.Limits.weakEqualizerIsWeakEqualizerstatement and proof · cited by 1
- CategoryTheory.Limits.weakEqualizer.lift.congr_simpstatement and proof · cited by 0
- CategoryTheory.Preadditive.hasWeakKernel_of_hasWeakEqualizerstatement and proof · cited by 0
- CategoryTheory.Preadditive.hasWeakEqualizers_of_hasWeakKernelsproof · cited by 0
- CategoryTheory.Limits.weakEqualizer.condition_assocstatement and proof · cited by 0