Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.Under.pushoutCongr_hom_app_left_fst_assoc

∀ {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 : P.HasPushoutsAlong f] {g : X ⟶ Y}
  [inst_3 : P.IsStableUnderCobaseChangeAlong f] [inst_4 : Q.IsStableUnderCobaseChange] (h : f = g) (A : P.Under Q X)
  {Z : T} (h_1 : ((CategoryTheory.MorphismProperty.Under.pushout P Q g).obj A).right ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pushout.inl A.hom f)
      (CategoryTheory.CategoryStruct.comp ((CategoryTheory.MorphismProperty.Under.pushoutCongr h).hom.app A).right
        h_1) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pushout.inl A.hom g) h_1

Defined in

Mathlib.CategoryTheory.MorphismProperty.OverAdjunction

Cited by

0 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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