Theorems · Definition · category theory

CategoryTheory.MorphismProperty.Over.pullback

{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) →
            [P.HasPullbacksAlong f] →
              [P.IsStableUnderBaseChangeAlong f] →
                [Q.IsStableUnderBaseChange] → CategoryTheory.Functor (P.Over Q Y) (P.Over Q X)

If P and Q are stable under base change and pullbacks along f exist for morphisms in P, this is the functor P.Over Q Y ⥤ P.Over Q X given by base change along f.

Defined in

Mathlib.CategoryTheory.MorphismProperty.OverAdjunction

Cited by

42 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MorphismProperty.IsMultiplicativeCategoryTheory.MorphismProperty.HasPullbacksAlongCategoryTheory.MorphismProperty.IsStableUnderBaseChangeAlongCategoryTheory.MorphismProperty.IsStableUnderBaseChange