Theorems · Definition · category theory

CategoryTheory.MorphismProperty.Over.mapId

{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] →
              [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) →
                      CategoryTheory.MorphismProperty.Over.map Q ⋯ ≅ CategoryTheory.Functor.id (P.Over Q X)

Over.map preserves identities.

Defined in

Mathlib.CategoryTheory.MorphismProperty.OverAdjunction

Cited by

4 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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