Theorems · Theorem · category theory

CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.exists_larger_subobject

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {G : C} [CategoryTheory.Abelian C],
  CategoryTheory.IsSeparator G →
    ∀ {X : C} (A : CategoryTheory.Subobject X),
      A ≠ ⊤ →
        ∃ A', ∃ (h : A < A'), (CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms G).pushouts (A.ofLE A' ⋯)

Defined in

Mathlib.CategoryTheory.Abelian.GrothendieckCategory.EnoughInjectives

Cited by

2 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Abelian