Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.Under.pushoutCompForgetIso_hom_app_right

∀ {T : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} T] {P Q : CategoryTheory.MorphismProperty T}
  [inst_1 : Q.IsMultiplicative] {X Y : T} (f : X ⟶ Y) [inst_2 : CategoryTheory.Limits.HasPushoutsAlong f]
  [inst_3 : P.IsStableUnderCobaseChangeAlong f] [inst_4 : Q.IsStableUnderCobaseChange] (X_1 : P.Under Q X),
  ((CategoryTheory.MorphismProperty.Under.pushoutCompForgetIso f).hom.app X_1).right =
    CategoryTheory.CategoryStruct.id (CategoryTheory.Limits.pushout X_1.hom f)

Defined in

Mathlib.CategoryTheory.MorphismProperty.OverAdjunction

Cited by

0 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MorphismProperty.IsMultiplicativeCategoryTheory.Limits.HasPushoutsAlongCategoryTheory.MorphismProperty.IsStableUnderCobaseChangeAlongCategoryTheory.MorphismProperty.IsStableUnderCobaseChange