Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.faithful_overPullback_of_isomorphisms_descendAlong

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {P : CategoryTheory.MorphismProperty C}
  [(CategoryTheory.MorphismProperty.isomorphisms C).DescendsAlong P] [P.IsStableUnderBaseChange]
  [inst_3 : CategoryTheory.Limits.HasPullbacks C] [CategoryTheory.Limits.HasEqualizers C] {S T : C} {f : T ⟶ S},
  P f → (CategoryTheory.Over.pullback f).Faithful

Defined in

Mathlib.CategoryTheory.MorphismProperty.Descent

Cited by

0 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MorphismProperty.DescendsAlongCategoryTheory.MorphismProperty.IsStableUnderBaseChangeCategoryTheory.Limits.HasPullbacksCategoryTheory.Limits.HasEqualizers