Theorems · Definition · category theory

CategoryTheory.MorphismProperty.Over.mapPullbackAdj

{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.IsStableUnderBaseChange] →
              (f : X ⟶ Y) →
                [inst_4 : P.HasPullbacksAlong f] →
                  [inst_5 : P.IsStableUnderBaseChangeAlong f] →
                    [Q.HasOfPostcompProperty Q] →
                      (hPf : P f) →
                        Q f →
                          (CategoryTheory.MorphismProperty.Over.map Q hPf ⊣
                            CategoryTheory.MorphismProperty.Over.pullback P Q f)

P.Over.map is left adjoint to P.Over.pullback if pullbacks 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

5 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.MorphismProperty.IsMultiplicativeCategoryTheory.MorphismProperty.IsStableUnderCompositionCategoryTheory.MorphismProperty.IsStableUnderBaseChangeCategoryTheory.MorphismProperty.HasPullbacksAlongCategoryTheory.MorphismProperty.IsStableUnderBaseChangeAlongCategoryTheory.MorphismProperty.HasOfPostcompProperty