Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.overPullbackMap

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {P : CategoryTheory.MorphismProperty C}
  [P.IsStableUnderBaseChange] {S S' : C} (f : S' ⟶ S) [inst_2 : CategoryTheory.Limits.HasPullbacksAlong f]
  {X Y : CategoryTheory.Over S} (g : X ⟶ Y),
  P (CategoryTheory.Over.Hom.left g) → P (CategoryTheory.Over.Hom.left ((CategoryTheory.Over.pullback f).map g))

Defined in

Mathlib.CategoryTheory.MorphismProperty.Limits

Cited by

2 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MorphismProperty.IsStableUnderBaseChangeCategoryTheory.Limits.HasPullbacksAlong