Theorems · Theorem · category theory
CategoryTheory.Preadditive.isCoseparator_iff
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C] (G : C),
CategoryTheory.IsCoseparator G ↔
∀ ⦃X Y : C⦄ (f : X ⟶ Y), (∀ (h : Y ⟶ G), CategoryTheory.CategoryStruct.comp f h = 0) → f = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- sub_eq_zeroproof · cited by 407
- CategoryTheory.Limits.zero_compproof · cited by 339
- CategoryTheory.Preadditive.sub_compproof · cited by 34
- CategoryTheory.IsCoseparatorstatement and proof · cited by 28
- CategoryTheory.isCoseparator_defproof · cited by 5
- CategoryTheory.IsCoseparator.defproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Abelian.has_injective_coseparatorproof · cited by 1