Theorems · Theorem · category theory
CategoryTheory.Limits.id_zero
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroObject C]
[inst_2 : CategoryTheory.Limits.HasZeroMorphisms C], CategoryTheory.CategoryStruct.id 0 = 0- Cited by
- 7 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 · cited by 32,603
- CategoryTheory.CategoryStruct.idstatement and proof · cited by 6,235
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.Limits.HasZeroObjectstatement and proof · cited by 1,298
- CategoryTheory.Limits.HasZeroObject.zero'statement · cited by 115
- CategoryTheory.Limits.HasZeroObject.from_zero_extproof · cited by 8
Cited by7
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.zero_of_source_iso_zeroproof · cited by 7
- CategoryTheory.Limits.zero_of_target_iso_zeroproof · cited by 4
- CategoryTheory.Functor.preservesFiniteLimits_of_preservesHomologyproof · cited by 4
- CategoryTheory.Functor.preservesFiniteColimits_of_preservesHomologyproof · cited by 2
- CategoryTheory.Pretriangulated.contractible_distinguished₂proof · cited by 1
- CategoryTheory.zero_not_simpleproof · cited by 0
- CategoryTheory.Functor.hasZeroObject_of_additiveproof · cited by 0