Theorems · Definition · category theory

CategoryTheory.MorphismProperty.Under.homMk

{T : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} T] →
    {P Q : CategoryTheory.MorphismProperty T} →
      {X : T} →
        [inst_1 : Q.IsMultiplicative] →
          {A B : P.Under Q X} →
            (f : A.right ⟶ B.right) →
              autoParam (CategoryTheory.CategoryStruct.comp A.hom f = B.hom)
                  CategoryTheory.MorphismProperty.Under.homMk._auto_1 →
                autoParam (Q f) CategoryTheory.MorphismProperty.Under.homMk._auto_3 → (A ⟶ B)

Make a morphism in P.Under Q X from a morphism in T with compatibilities.

Defined in

Mathlib.CategoryTheory.MorphismProperty.Comma

Cited by

4 results in Mathlib

Foundations

Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MorphismProperty.IsMultiplicative