Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.overEquivOfIsInitial_counitIso

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] (P Q : CategoryTheory.MorphismProperty C)
  [inst_1 : P.ContainsIdentities] [inst_2 : Q.IsMultiplicative] [inst_3 : Q.RespectsIso]
  [inst_4 : CategoryTheory.Limits.HasStrictInitialObjects C] (X : C) (h : CategoryTheory.Limits.IsInitial X),
  (CategoryTheory.MorphismProperty.overEquivOfIsInitial.{w, v_1, u_1} P Q X h).counitIso =
    CategoryTheory.Iso.refl
      ((CategoryTheory.Functor.fromPUnit
            (CategoryTheory.MorphismProperty.Over.mk Q (CategoryTheory.CategoryStruct.id X) ⋯)).comp
        (CategoryTheory.Functor.star (P.Over Q X)))

Defined in

Mathlib.CategoryTheory.Comma.Over.StrictInitial

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.MorphismProperty.ContainsIdentitiesCategoryTheory.MorphismProperty.IsMultiplicativeCategoryTheory.MorphismProperty.RespectsIsoCategoryTheory.Limits.HasStrictInitialObjects