Theorems · Theorem · category theory

CategoryTheory.Abelian.has_injective_coseparator

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [CategoryTheory.Abelian C] [CategoryTheory.Limits.HasLimits C]
  [CategoryTheory.EnoughInjectives C] (G : C),
  CategoryTheory.IsSeparator G → ∃ G, CategoryTheory.Injective G ∧ CategoryTheory.IsCoseparator G

Defined in

Mathlib.CategoryTheory.Generator.Abelian

Cited by

1 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.Limits.HasLimitsCategoryTheory.EnoughInjectives