Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.Over.map_obj_left

∀ {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} [inst_2 : P.IsStableUnderComposition]
  {f : X ⟶ Y} (hPf : P f)
  (X_1 :
    CategoryTheory.MorphismProperty.Comma (CategoryTheory.Functor.id T) (CategoryTheory.Functor.fromPUnit X) P Q ⊤),
  ((CategoryTheory.MorphismProperty.Over.map Q hPf).obj X_1).left = X_1.left

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