Theorems · Theorem · category theory
CategoryTheory.Limits.isZero_zero
∀ (C : Type u) [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroObject C],
CategoryTheory.Limits.IsZero 0- Cited by
- 34 results in Mathlib
- Foundations
- Depth 10 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
- CategoryTheory.Limits.HasZeroObjectstatement and proof · cited by 1,298
- CategoryTheory.Limits.IsZerostatement · cited by 306
- CategoryTheory.Limits.HasZeroObject.zero'statement · cited by 115
- CategoryTheory.Limits.HasZeroObject.zeroproof · cited by 1
Cited by41
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.exact_iff_epiproof · cited by 8
- CategoryTheory.ShortComplex.exact_iff_monoproof · cited by 8
- CategoryTheory.Limits.HasZeroObject.from_zero_extproof · cited by 8
- CategoryTheory.Limits.IsZero.isoZeroproof · cited by 7
- HomologicalComplex.isZero_single_obj_Xproof · cited by 7
- CategoryTheory.Abelian.Ext.zero_homproof · cited by 6
- CategoryTheory.ShortComplex.Exact.leftHomologyDataOfIsLimitKernelForkproof · cited by 5
- CategoryTheory.ShortComplex.Splitting.leftHomologyDataproof · cited by 5
- CategoryTheory.ShortComplex.Splitting.rightHomologyDataproof · cited by 5
- CategoryTheory.Limits.HasZeroObject.to_zero_extproof · cited by 5
- CategoryTheory.Limits.HasZeroObject.zeroIsInitialproof · cited by 5