Theorems · Definition · category theory

CategoryTheory.StructuredArrow.homMk

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        {S : D} →
          {T : CategoryTheory.Functor C D} →
            {f f' : CategoryTheory.StructuredArrow S T} →
              (g : f.right ⟶ f'.right) →
                autoParam (CategoryTheory.CategoryStruct.comp f.hom (T.map g) = f'.hom)
                    CategoryTheory.StructuredArrow.homMk._auto_1 →
                  (f ⟶ f')

To construct a morphism of structured arrows, we need a morphism of the objects underlying the target, and to check that the triangle commutes.

Defined in

Mathlib.CategoryTheory.Comma.StructuredArrow.Basic

Cited by

47 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category