Theorems · Theorem · category theory
CategoryTheory.Limits.IsZero.eq_of_src
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C},
CategoryTheory.Limits.IsZero X → ∀ (f g : X ⟶ Y), f = g- Cited by
- 57 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses Classical.choice
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.IsZerostatement and proof · cited by 306
- CategoryTheory.Limits.IsZero.eq_toproof · cited by 2
Cited by57
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.IsZero.iff_id_eq_zeroproof · cited by 40
- CategoryTheory.Limits.IsZero.of_isoproof · cited by 35
- HomologicalComplex.from_single_hom_extproof · cited by 8
- CategoryTheory.ShortComplex.exact_of_isZero_X₂proof · cited by 8
- CategoryTheory.Limits.HasZeroObject.from_zero_extproof · cited by 8
- CategoryTheory.Limits.IsZero.eq_zero_of_srcproof · cited by 7
- CategoryTheory.Abelian.Ext.zero_homproof · cited by 6
- quasiIsoAt_iff_exactAtproof · cited by 5
- CategoryTheory.Limits.IsZero.opproof · cited by 5
- CategoryTheory.Limits.IsZero.unopproof · cited by 5
- CategoryTheory.Functor.isZeroproof · cited by 5
- CategoryTheory.Preadditive.epi_of_isZero_cokernel'proof · cited by 4