Theorems · Theorem · category theory

CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.largerSubobject.congr_simp

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {G G_1 : C} (e_G : G = G_1) [inst_1 : CategoryTheory.Abelian C]
  (hG : CategoryTheory.IsSeparator G) {X : C} (A A_1 : CategoryTheory.Subobject X),
  A = A_1 →
    CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.largerSubobject hG A =
      CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.largerSubobject ⋯ A_1

Defined in: Mathlib.CategoryTheory.Abelian.GrothendieckCategory.EnoughInjectives
Cited by: 0 results in Mathlib
Foundations: Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian

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CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Abelianstatement and proof · cited by 1,753
CategoryTheory.Subobjectstatement and proof · cited by 385
CategoryTheory.IsSeparatorstatement and proof · cited by 58
CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.largerSubobjectstatement and proof · cited by 10

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