Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.Over.mapPullbackAdj_unit_app

∀ {T : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} T] (P Q : CategoryTheory.MorphismProperty T)
  [inst_1 : Q.IsMultiplicative] {X Y : T} [inst_2 : P.IsStableUnderComposition] [inst_3 : Q.IsStableUnderBaseChange]
  (f : X ⟶ Y) [inst_4 : P.HasPullbacksAlong f] [inst_5 : P.IsStableUnderBaseChangeAlong f]
  [inst_6 : Q.HasOfPostcompProperty Q] (hPf : P f) (hQf : Q f) (A : P.Over Q X),
  (CategoryTheory.MorphismProperty.Over.mapPullbackAdj P Q f hPf hQf).unit.app A =
    CategoryTheory.MorphismProperty.Over.homMk
      (CategoryTheory.Limits.pullback.lift (CategoryTheory.CategoryStruct.id A.left) A.hom ⋯) ⋯ ⋯

Defined in

Mathlib.CategoryTheory.MorphismProperty.OverAdjunction

Cited by

0 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MorphismProperty.IsMultiplicativeCategoryTheory.MorphismProperty.IsStableUnderCompositionCategoryTheory.MorphismProperty.IsStableUnderBaseChangeCategoryTheory.MorphismProperty.HasPullbacksAlongCategoryTheory.MorphismProperty.IsStableUnderBaseChangeAlongCategoryTheory.MorphismProperty.HasOfPostcompProperty