Theorems · Theorem · category theory

CategoryTheory.Limits.weakEqualizer.condition

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {X Y : C} (f g : X ⟶ Y)
  [inst_1 : CategoryTheory.Limits.HasWeakEqualizer f g],
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.weakEqualizer.ι f g) f =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.weakEqualizer.ι f g) g

Defined in: Mathlib.CategoryTheory.Limits.WeakLimits.WeakEqualizers
Cited by: 3 results in Mathlib
Foundations: Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasWeakEqualizer

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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.Fork.conditionproof · cited by 11
CategoryTheory.Limits.weakLimit.coneproof · cited by 10
CategoryTheory.Limits.HasWeakEqualizerstatement and proof · cited by 10
CategoryTheory.Limits.weakEqualizer.ιstatement · cited by 9
CategoryTheory.Limits.weakEqualizerstatement · cited by 7

Cited by4

Results whose statement or proof uses this declaration.

CategoryTheory.Preadditive.hasWeakEqualizer_of_hasWeakKernelproof · cited by 1
CategoryTheory.Limits.weakEqualizerIsWeakEqualizerstatement · cited by 1
CategoryTheory.Limits.hasWeakLimit_cospan_of_hasLimit_pair_of_hasWeakLimit_parallelPairproof · cited by 0
CategoryTheory.Limits.weakEqualizer.condition_assocproof · cited by 0