Theorems · Definition · category theory

CategoryTheory.MorphismProperty.Under.map

{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 : T} →
            [P.IsStableUnderComposition] → {f : X ⟶ Y} → P f → CategoryTheory.Functor (P.Under Q Y) (P.Under Q X)

If P is stable under composition and f : X ⟶ Y satisfies P, this is the functor P.Under Q Y ⥤ P.Under Q X given by composing with f.

Defined in

Mathlib.CategoryTheory.MorphismProperty.OverAdjunction

Cited by

11 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MorphismProperty.IsMultiplicativeCategoryTheory.MorphismProperty.IsStableUnderComposition