Theorems · Theorem · category theory

CategoryTheory.Limits.hasEqualizer_of_common_retraction

∀ (C : Type u) [inst : CategoryTheory.Category.{v, u} C] [CategoryTheory.Limits.HasCoreflexiveEqualizers C] {A B : C}
  {f g : A ⟶ B} (r : B ⟶ A),
  CategoryTheory.CategoryStruct.comp f r = CategoryTheory.CategoryStruct.id A →
    CategoryTheory.CategoryStruct.comp g r = CategoryTheory.CategoryStruct.id A → CategoryTheory.Limits.HasEqualizer f g

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Reflexive

Cited by

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Foundations

Depth 21 from the axioms · uses propext

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasCoreflexiveEqualizers