Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.Over.mapComp_hom_app_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 Z : T}
  [inst_2 : P.IsStableUnderComposition] {f : X ⟶ Y} (hf : P f) {g : Y ⟶ Z} (hg : P g) [inst_3 : Q.RespectsIso]
  (fg : optParam (X ⟶ Z) (CategoryTheory.CategoryStruct.comp f g))
  (hfg : autoParam (fg = CategoryTheory.CategoryStruct.comp f g) CategoryTheory.MorphismProperty.Over.mapComp._auto_1)
  (X_1 : P.Over Q X),
  ((CategoryTheory.MorphismProperty.Over.mapComp Q hf hg fg hfg).hom.app X_1).left =
    CategoryTheory.CategoryStruct.id X_1.left

Defined in

Mathlib.CategoryTheory.MorphismProperty.OverAdjunction

Cited by

0 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MorphismProperty.IsMultiplicativeCategoryTheory.MorphismProperty.IsStableUnderCompositionCategoryTheory.MorphismProperty.RespectsIso