Theorems · Definition · category theory

CategoryTheory.Limits.isLimitOfHasEqualizerOfPreservesLimit

{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] →
                [CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.parallelPair f g) G] →
                  CategoryTheory.Limits.IsLimit
                    (CategoryTheory.Limits.Fork.ofι (G.map (CategoryTheory.Limits.equalizer.ι f g)) ⋯)

If G preserves equalizers and C has them, then the fork constructed of the mapped morphisms of a fork is a limit.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers

Cited by

0 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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