Theorems · Theorem · category theory

CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.exists_ordinal

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {G : C} [inst_1 : CategoryTheory.Abelian C]
  (hG : CategoryTheory.IsSeparator G) {X : C} [inst_2 : CategoryTheory.IsGrothendieckAbelian.{w, v, u} C]
  (A₀ : CategoryTheory.Subobject X),
  ∃ o j, transfiniteIterate (CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.largerSubobject hG) j A₀ = ⊤

Defined in

Mathlib.CategoryTheory.Abelian.GrothendieckCategory.EnoughInjectives

Cited by

1 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.IsGrothendieckAbelian