Theorems · Theorem · category theory
CategoryTheory.Limits.zero_of_source_iso_zero
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroObject C]
[inst_2 : CategoryTheory.Limits.HasZeroMorphisms C] {X Y : C} (f : X ⟶ Y) (i : X ≅ 0), f = 0- Cited by
- 7 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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.Iso.homproof · cited by 7,684
- CategoryTheory.Iso.invproof · cited by 6,514
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Isostatement and proof · cited by 3,963
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.Category.id_compproof · cited by 1,998
- CategoryTheory.Limits.HasZeroObjectstatement and proof · cited by 1,298
- CategoryTheory.Limits.comp_zeroproof · cited by 365
- CategoryTheory.Limits.zero_compproof · cited by 339
Cited by7
Results whose statement or proof uses this declaration.
- CategoryTheory.MonoOver.bot_arrow_eq_zeroproof · cited by 2
- CategoryTheory.Subobject.bot_arrowproof · cited by 1
- CategoryTheory.Limits.isIso_of_source_target_iso_zeroproof · cited by 1
- CategoryTheory.Preadditive.mono_of_kernel_iso_zeroproof · cited by 0
- CategoryTheory.Limits.zero_of_source_iso_zero'proof · cited by 0
- CategoryTheory.Limits.kernel.ι_of_monoproof · cited by 0
- CategoryTheory.Limits.epi_of_target_iso_zeroproof · cited by 0