Theorems · Theorem · category theory
CategoryTheory.Limits.IsZero.iff_isSplitMono_eq_zero
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] {X Y : C}
(f : X ⟶ Y) [CategoryTheory.IsSplitMono f], CategoryTheory.Limits.IsZero X ↔ f = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext, Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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.compproof · cited by 17,999
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.Category.id_compproof · cited by 1,998
- CategoryTheory.Limits.zero_compproof · cited by 339
- CategoryTheory.Limits.IsZerostatement · cited by 306
- CategoryTheory.Limits.IsZero.iff_id_eq_zeroproof · cited by 40
- CategoryTheory.IsSplitMonostatement and proof · cited by 33
- CategoryTheory.IsSplitMono.idproof · cited by 6
- CategoryTheory.retraction.congr_simpproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.indecomposable_of_simpleproof · cited by 0