Theorems · Definition · category theory

CategoryTheory.Limits.PreservesEqualizer.iso

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (G : CategoryTheory.Functor C D) →
          {X Y : C} →
            (f g : X ⟶ Y) →
              [inst_2 : CategoryTheory.Limits.HasEqualizer f g] →
                [inst_3 : CategoryTheory.Limits.HasEqualizer (G.map f) (G.map g)] →
                  [CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.parallelPair f g) G] →
                    G.obj (CategoryTheory.Limits.equalizer f g) ≅ CategoryTheory.Limits.equalizer (G.map f) (G.map g)

If G preserves the equalizer of (f,g), then the equalizer comparison map for G at (f,g) is an isomorphism.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers

Cited by

3 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasEqualizerCategoryTheory.Limits.HasEqualizerCategoryTheory.Limits.PreservesLimit