Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.underPushoutMap

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {P : CategoryTheory.MorphismProperty C}
  [P.IsStableUnderCobaseChange] {S S' : C} (f : S' ⟶ S) [inst_2 : CategoryTheory.Limits.HasPushoutsAlong f]
  {X Y : CategoryTheory.Under S'} (g : X ⟶ Y),
  P (CategoryTheory.Under.Hom.right g) → P (CategoryTheory.Under.Hom.right ((CategoryTheory.Under.pushout f).map g))

Defined in

Mathlib.CategoryTheory.MorphismProperty.Limits

Cited by

1 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MorphismProperty.IsStableUnderCobaseChangeCategoryTheory.Limits.HasPushoutsAlong