Theorems · Theorem · category theory
CategoryTheory.Limits.IsZero.eq_zero_of_src
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] {X Y : C},
CategoryTheory.Limits.IsZero X → ∀ (f : X ⟶ Y), f = 0- Cited by
- 7 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_srcproof · cited by 57
Cited by7
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.SnakeInput.mono_δproof · cited by 3
- FDRep.simple_iff_end_is_rank_oneproof · cited by 1
- ModuleCat.hasProjectiveDimensionLT_of_forall_finiteproof · cited by 1
- ModuleCat.exists_isRegular_of_exists_subsingleton_extproof · cited by 1
- ModuleCat.subsingleton_ext_of_exists_isRegularproof · cited by 1
- CategoryTheory.ShortComplex.Exact.isZero_of_both_isZeroproof · cited by 0
- CategoryTheory.Limits.IsZero.of_epiproof · cited by 0