Theorems · Theorem · category theory
CategoryTheory.Limits.isIso_of_source_target_iso_zero
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [CategoryTheory.Limits.HasZeroMorphisms C]
[inst_2 : CategoryTheory.Limits.HasZeroObject C] {X Y : C} (f : X ⟶ Y) (i : X ≅ 0) (j : Y ≅ 0), CategoryTheory.IsIso f- Cited by
- 1 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.Isostatement and proof · cited by 3,963
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.Limits.HasZeroObjectstatement and proof · cited by 1,298
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- Equiv.invFunproof · cited by 163
- CategoryTheory.Limits.HasZeroObject.zero'statement · cited by 115
- CategoryTheory.Limits.zero_of_source_iso_zeroproof · cited by 7
- CategoryTheory.Limits.isIsoZeroEquivIsoZeroproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- TopCat.Sheaf.isZero_iff_stalkFunctor_obj_isZeroproof · cited by 1