Theorems · Definition · category theory

CategoryTheory.MorphismProperty.Under.pushout

{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.HasPushoutsAlong f] →
              [P.IsStableUnderCobaseChangeAlong f] →
                [Q.IsStableUnderCobaseChange] → CategoryTheory.Functor (P.Under Q X) (P.Under Q Y)

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

Defined in

Mathlib.CategoryTheory.MorphismProperty.OverAdjunction

Cited by

15 results in Mathlib

Foundations

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

Assumes

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