Theorems · Definition · category theory

CategoryTheory.Limits.Trident.mkHom

{J : Type w} →
  {C : Type u} →
    [inst : CategoryTheory.Category.{v, u} C] →
      {X Y : C} →
        {f : J → (X ⟶ Y)} →
          [Nonempty J] →
            {s t : CategoryTheory.Limits.Trident f} →
              (k : s.pt ⟶ t.pt) →
                autoParam (CategoryTheory.CategoryStruct.comp k t.ι = s.ι) CategoryTheory.Limits.Trident.mkHom._auto_1 →
                  (s ⟶ t)

Helper function for constructing morphisms between wide equalizer tridents.

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

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Cites9

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.compstatement and proof · cited by 17,999
CategoryTheory.Limits.Cone.ptstatement and proof · cited by 1,298
CategoryTheory.Limits.WalkingParallelFamilystatement · cited by 61
CategoryTheory.Limits.parallelFamilystatement · cited by 58
CategoryTheory.Limits.Tridentstatement and proof · cited by 15
CategoryTheory.Limits.Trident.ιstatement and proof · cited by 15

Cited by5

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.Trident.extproof · cited by 2
CategoryTheory.Limits.Trident.ext_homstatement · cited by 0
CategoryTheory.Limits.Trident.ext_invstatement · cited by 0
CategoryTheory.Limits.Trident.mkHom_homstatement and proof · cited by 0
CategoryTheory.Limits.Trident.mkHom.congr_simpstatement and proof · cited by 0