Theorems · Definition · category theory

CategoryTheory.Limits.Fork.op

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {X Y : C} → {f g : X ⟶ Y} → CategoryTheory.Limits.Fork f g → CategoryTheory.Limits.Cofork f.op g.op

The obvious map Fork f g → Cofork f.op g.op

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers
Cited by: 7 results in Mathlib
Foundations: Depth 30 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.

Cites14

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.objproof · cited by 19,642
Oppositestatement · cited by 8,081
CategoryTheory.Iso.homproof · cited by 7,684
Quiver.Hom.opstatement · cited by 1,948
CategoryTheory.Equivalence.functorproof · cited by 1,268
CategoryTheory.Limits.Cocone.precomposeproof · cited by 87
CategoryTheory.Limits.Forkstatement and proof · cited by 85
CategoryTheory.Limits.Coforkstatement · cited by 80
CategoryTheory.Limits.Cocone.whiskerproof · cited by 40
CategoryTheory.Limits.walkingParallelPairOpEquivproof · cited by 23

Cited by11

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.Fork.op_πstatement · cited by 2
CategoryTheory.Limits.Cofork.unopOpIsostatement and proof · cited by 0
CategoryTheory.Limits.Cofork.unop_op_πstatement · cited by 0
CategoryTheory.Limits.Fork.ofιOpIsoOfπstatement and proof · cited by 0
CategoryTheory.Limits.Fork.opUnopIsostatement and proof · cited by 0
CategoryTheory.Limits.Fork.op_ptstatement and proof · cited by 0
CategoryTheory.Limits.Fork.op_unop_ιstatement and proof · cited by 0
CategoryTheory.Limits.Fork.op_ι_appstatement and proof · cited by 0
CategoryTheory.Limits.Fork.op_ι_app_onestatement · cited by 0
CategoryTheory.Limits.Fork.op_ι_app_zerostatement · cited by 0
CategoryTheory.Limits.Fork.isLimitEquivIsColimitOpstatement and proof · cited by 0