Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.Under.pushoutComp_inv_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 Z : T} (f : X ⟶ Y) (g : Y ⟶ Z) [inst_2 : P.IsStableUnderCobaseChangeAlong f]
  [inst_3 : P.IsStableUnderCobaseChangeAlong g] [inst_4 : P.HasPushoutsAlong f] [inst_5 : P.HasPushoutsAlong g]
  [inst_6 : Q.RespectsIso] [inst_7 : Q.IsStableUnderCobaseChange]
  (fg : optParam (X ⟶ Z) (CategoryTheory.CategoryStruct.comp f g))
  (hfg :
    autoParam (fg = CategoryTheory.CategoryStruct.comp f g) CategoryTheory.MorphismProperty.Under.pushoutComp._auto_1)
  (X_1 : P.Under Q X),
  ((CategoryTheory.MorphismProperty.Under.pushoutComp f g fg hfg).inv.app X_1).right =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pushoutLeftPushoutInrIso X_1.hom f g).hom
      (CategoryTheory.Limits.pushout.map X_1.hom (CategoryTheory.CategoryStruct.comp f g) X_1.hom fg
        (CategoryTheory.CategoryStruct.id X_1.right) (CategoryTheory.CategoryStruct.id Z)
        (CategoryTheory.CategoryStruct.id X) ⋯ ⋯)

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.IsStableUnderCobaseChangeAlongCategoryTheory.MorphismProperty.IsStableUnderCobaseChangeAlongCategoryTheory.MorphismProperty.HasPushoutsAlongCategoryTheory.MorphismProperty.HasPushoutsAlongCategoryTheory.MorphismProperty.RespectsIsoCategoryTheory.MorphismProperty.IsStableUnderCobaseChange