Theorems · Definition · category theory

CategoryTheory.Limits.opParallelPairIso

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {X Y : C} →
      (f g : X ⟶ Y) →
        (CategoryTheory.Limits.parallelPair f g).op ≅
          CategoryTheory.Limits.walkingParallelPairOpEquiv.inverse.comp (CategoryTheory.Limits.parallelPair f.op g.op)

The canonical isomorphism relating (parallelPair f g).op and parallelPair f.op g.op

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers
Cited by: 4 results in Mathlib
Foundations: Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites21

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.Functorstatement · cited by 16,252
Oppositestatement · cited by 8,081
CategoryTheory.Functor.compstatement · cited by 6,529
CategoryTheory.Isostatement · cited by 3,963
Quiver.Hom.opstatement · cited by 1,948
CategoryTheory.Equivalence.functorproof · cited by 1,268
CategoryTheory.Equivalence.inversestatement and proof · cited by 1,130
CategoryTheory.Functor.opstatement and proof · cited by 997
CategoryTheory.Iso.symmproof · cited by 993
CategoryTheory.Limits.WalkingParallelPairstatement · cited by 781

Cited by8

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.Cofork.unopproof · cited by 5
CategoryTheory.Limits.Fork.unopproof · cited by 5
CategoryTheory.Limits.opParallelPairIso_hom_app_zerostatement · cited by 2
CategoryTheory.Limits.opParallelPairIso_inv_app_onestatement · cited by 2
CategoryTheory.Limits.opParallelPairIso_hom_app_onestatement · cited by 1
CategoryTheory.Limits.opParallelPairIso_inv_app_zerostatement · cited by 1
CategoryTheory.Limits.Cofork.isColimitEquivIsLimitOpproof · cited by 0
CategoryTheory.Limits.Cofork.isColimitEquivIsLimitUnopproof · cited by 0