Theorems · Theorem · category theory

CategoryTheory.Limits.PreservesEqualizer.of_iso_comparison

∀ {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)]
  [i : CategoryTheory.IsIso (CategoryTheory.Limits.equalizerComparison f g G)],
  CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.parallelPair f g) G

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

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers

Cited by

0 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasEqualizerCategoryTheory.Limits.HasEqualizerCategoryTheory.IsIso