Theorems · Definition · category theory

CategoryTheory.MorphismProperty.Under.pushoutCompForgetIso

{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] →
                  (CategoryTheory.MorphismProperty.Under.pushout P Q f).comp
                      (CategoryTheory.MorphismProperty.Under.forget P Q Y) ≅
                    (CategoryTheory.MorphismProperty.Under.forget P Q X).comp (CategoryTheory.Under.pushout f)

MorphismProperty.Under.pushout commutes with MorphismProperty.Under.forget.

Defined in

Mathlib.CategoryTheory.MorphismProperty.OverAdjunction

Cited by

4 results in Mathlib

Foundations

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

Assumes

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