Theorems · Theorem · category theory

CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.top_mem_range

∀ {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) {J : Type w} [inst_3 : LinearOrder J] [OrderBot J] [inst_5 : SuccOrder J]
  [inst_6 : WellFoundedLT J],
  HasCardinalLT (CategoryTheory.Subobject X) (Cardinal.mk J) →
    ∃ j, transfiniteIterate (CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.largerSubobject hG) j A₀ = ⊤

Defined in

Mathlib.CategoryTheory.Abelian.GrothendieckCategory.EnoughInjectives

Cited by

1 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.IsGrothendieckAbelianLinearOrderOrderBotSuccOrderWellFoundedLT