Theorems · Theorem · category theory

CategoryTheory.Limits.opParallelPairIso_inv_app_zero

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} (f g : X ⟶ Y),
  (CategoryTheory.Limits.opParallelPairIso f g).inv.app (Opposite.op CategoryTheory.Limits.WalkingParallelPair.zero) =
    CategoryTheory.CategoryStruct.id
      ((CategoryTheory.Limits.walkingParallelPairOpEquiv.inverse.comp
            (CategoryTheory.Limits.parallelPair f.op g.op)).obj
        (Opposite.op CategoryTheory.Limits.WalkingParallelPair.zero))

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers

Cited by

1 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category