Theorems · Definition · category theory

CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.largerSubobject

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {G : C} →
      [CategoryTheory.Abelian C] →
        CategoryTheory.IsSeparator G → {X : C} → CategoryTheory.Subobject X → CategoryTheory.Subobject X

Assuming G : C is a generator, X : C, and A : Subobject X, this is a subobject of X which is ⊤ if A = ⊤, and otherwise it is a larger subobject given by the lemma exists_larger_subobject. The inclusion of A in largerSubobject hG A is a pushout of a monomorphism in the family generatingMonomorphisms G (see pushouts_ofLE_le_largerSubobject).

Defined in

Mathlib.CategoryTheory.Abelian.GrothendieckCategory.EnoughInjectives

Cited by

10 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Abelian