Theorems · Theorem · category theory

CategoryTheory.ConcreteCategory.mono_iff_injective_of_preservesPullback

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {FC : C → C → Type u_1} {CC : C → Type w}
  [inst_1 : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)] [inst_2 : CategoryTheory.ConcreteCategory C FC] {X Y : C}
  (f : X ⟶ Y)
  [CategoryTheory.Limits.PreservesLimitsOfShape CategoryTheory.Limits.WalkingCospan (CategoryTheory.forget C)],
  CategoryTheory.Mono f ↔ Function.Injective ⇑(CategoryTheory.ConcreteCategory.hom f)

Defined in

Mathlib.CategoryTheory.ConcreteCategory.EpiMono

Cited by

4 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategoryCategoryTheory.Limits.PreservesLimitsOfShape