Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.Under.map_comp

∀ {T : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} T] {P : CategoryTheory.MorphismProperty T}
  (Q : CategoryTheory.MorphismProperty T) [inst_1 : Q.IsMultiplicative] {X Y Z : T}
  [inst_2 : P.IsStableUnderComposition] {f : X ⟶ Y} (hf : P f) {g : Y ⟶ Z} (hg : P g),
  CategoryTheory.MorphismProperty.Under.map Q ⋯ =
    (CategoryTheory.MorphismProperty.Under.map Q hg).comp (CategoryTheory.MorphismProperty.Under.map Q hf)

Defined in

Mathlib.CategoryTheory.MorphismProperty.OverAdjunction

Cited by

0 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MorphismProperty.IsMultiplicativeCategoryTheory.MorphismProperty.IsStableUnderComposition