Theorems · Definition · category theory

CategoryTheory.MorphismProperty.Under.mapPushoutAdj

{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.IsStableUnderCobaseChange] →
              (f : X ⟶ Y) →
                [inst_4 : P.HasPushoutsAlong f] →
                  [inst_5 : P.IsStableUnderCobaseChangeAlong f] →
                    [Q.HasOfPrecompProperty Q] →
                      (hPf : P f) →
                        Q f →
                          (CategoryTheory.MorphismProperty.Under.pushout P Q f ⊣
                            CategoryTheory.MorphismProperty.Under.map Q hPf)

P.Under.pushout is left adjoint to P.Under.map if pushouts of morphisms satisfying P exist along f and are also in P, and f is in both P and Q.

Defined in

Mathlib.CategoryTheory.MorphismProperty.OverAdjunction

Cited by

3 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MorphismProperty.IsMultiplicativeCategoryTheory.MorphismProperty.IsStableUnderCompositionCategoryTheory.MorphismProperty.IsStableUnderCobaseChangeCategoryTheory.MorphismProperty.HasPushoutsAlongCategoryTheory.MorphismProperty.IsStableUnderCobaseChangeAlongCategoryTheory.MorphismProperty.HasOfPrecompProperty