Theorems · Theorem · category theory

CategoryTheory.IsGrothendieckAbelian.GabrielPopescu.full

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
  [CategoryTheory.IsGrothendieckAbelian.{v, v, u} C] (G : C),
  CategoryTheory.IsSeparator G → (CategoryTheory.preadditiveCoyonedaObj G).Full

Faithfulness follows because G is a separator, see isSeparator_iff_faithful_preadditiveCoyonedaObj.

Defined in

Mathlib.CategoryTheory.Abelian.GrothendieckCategory.ModuleEmbedding.GabrielPopescu

Cited by

0 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.IsGrothendieckAbelian