Theorems · Definition · category theory

CategoryTheory.Limits.Fork.mkHom

{C : Type u} →
  {X Y : C} →
    [inst : CategoryTheory.Category.{v, u} C] →
      {f g : X ⟶ Y} →
        {s t : CategoryTheory.Limits.Fork f g} →
          (k : s.pt ⟶ t.pt) → CategoryTheory.CategoryStruct.comp k t.ι = s.ι → (s ⟶ t)

Helper function for constructing morphisms between equalizer forks.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Equalizers
Cited by: 4 results in Mathlib
Foundations: Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites8

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.CategoryStruct.compstatement and proof · cited by 17,999
CategoryTheory.Limits.Cone.ptstatement and proof · cited by 1,298
CategoryTheory.Limits.WalkingParallelPairstatement · cited by 781
CategoryTheory.Limits.parallelPairstatement · cited by 766
CategoryTheory.Limits.Fork.ιstatement and proof · cited by 162
CategoryTheory.Limits.Forkstatement and proof · cited by 85

Cited by5

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.Fork.extproof · cited by 7
CategoryTheory.Limits.Fork.mkHom_homstatement and proof · cited by 0
CategoryTheory.Limits.Fork.ext_homstatement · cited by 0
CategoryTheory.Limits.Fork.ext_invstatement · cited by 0
CategoryTheory.Limits.Fork.mkHom.congr_simpstatement and proof · cited by 0