Theorems · Theorem · category theory
CategoryTheory.Limits.IsZero.eq_zero_of_tgt
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] {X Y : C},
CategoryTheory.Limits.IsZero Y → ∀ (f : X ⟶ Y), f = 0- Cited by
- 8 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.Limits.IsZerostatement and proof · cited by 306
- CategoryTheory.Limits.IsZero.eq_of_tgtproof · cited by 46
Cited by8
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.SnakeInput.epi_δproof · cited by 3
- ModuleCat.hasProjectiveDimensionLT_of_forall_finiteproof · cited by 1
- ModuleCat.exists_isRegular_of_exists_subsingleton_extproof · cited by 1
- ModuleCat.projectiveDimension_quotSMulTop_eq_succ_of_isSMulRegularproof · cited by 1
- CategoryTheory.Abelian.Preradical.isIso_toColon_hom_left_app_iffproof · cited by 1
- CategoryTheory.Limits.IsZero.hasInjectiveDimensionLT_zeroproof · cited by 1
- CategoryTheory.Limits.IsZero.of_monoproof · cited by 0
- CategoryTheory.ShortComplex.Exact.isZero_of_both_isZeroproof · cited by 0