Theorems · Theorem · category theory

CategoryTheory.JointlyReflectIsomorphisms.mono

∀ {C : Type u_1} [inst : CategoryTheory.Category.{u_4, u_1} C] {I : Type u_2} {D : I → Type u_3}
  [inst_1 : (i : I) → CategoryTheory.Category.{u_5, u_3} (D i)] {F : (i : I) → CategoryTheory.Functor C (D i)},
  CategoryTheory.JointlyReflectIsomorphisms F →
    ∀ {X Y : C} (f : X ⟶ Y) [hf : ∀ (i : I), CategoryTheory.Mono ((F i).map f)]
      [∀ (i : I), CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.cospan f f) (F i)]
      [CategoryTheory.Limits.HasPullback f f], CategoryTheory.Mono f

Defined in

Mathlib.CategoryTheory.Functor.ReflectsIso.Jointly

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoCategoryTheory.Limits.PreservesLimitCategoryTheory.Limits.HasPullback