Theorems · Theorem · category theory

CategoryTheory.Limits.opParallelPairIso_hom_app_one

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

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

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Cites29

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objstatement · cited by 19,642
CategoryTheory.CategoryStruct.compproof · cited by 17,999
CategoryTheory.Functorstatement · cited by 16,252
Oppositestatement · cited by 8,081
CategoryTheory.Iso.homstatement and proof · cited by 7,684
CategoryTheory.NatTrans.appstatement and proof · cited by 7,406
CategoryTheory.Functor.compstatement · cited by 6,529
CategoryTheory.CategoryStruct.idstatement and proof · cited by 6,235
CategoryTheory.Category.comp_idproof · cited by 2,119
Quiver.Hom.opstatement and proof · cited by 1,948

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.Cofork.unop_π_app_oneproof · cited by 0