Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.Over.mapId_inv_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] [inst_2 : P.IsStableUnderComposition]
  [inst_3 : P.IsMultiplicative] [inst_4 : Q.RespectsIso] (X : T)
  (f : optParam (X ⟶ X) (CategoryTheory.CategoryStruct.id X))
  (hf : autoParam (f = CategoryTheory.CategoryStruct.id X) CategoryTheory.MorphismProperty.Over.mapId._auto_1)
  (X_1 : P.Over Q X),
  ((CategoryTheory.MorphismProperty.Over.mapId Q X f hf).inv.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.IsMultiplicativeCategoryTheory.MorphismProperty.RespectsIso