Theorems · Theorem · category theory
CategoryTheory.Limits.comp_zero
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] {X Y : C}
{f : X ⟶ Y} {Z : C}, CategoryTheory.CategoryStruct.comp f 0 = 0- Cited by
- 365 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 16 definitions · uses no axioms
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
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.Limits.HasZeroMorphisms.comp_zeroproof · cited by 9
Cited by367
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.IsZero.iff_id_eq_zeroproof · cited by 40
- HomologicalComplex.d_comp_dproof · cited by 36
- HomologicalComplex.Hom.commproof · cited by 29
- CategoryTheory.Limits.kernelIsKernelstatement · cited by 24
- CategoryTheory.ShortComplex.exact_iff_exact_up_to_refinementsproof · cited by 14
- CategoryTheory.ShortComplex.homologyι_comp_fromOpcyclesproof · cited by 11
- CochainComplex.HomComplex.δ_shapeproof · cited by 11
- CategoryTheory.ShortComplex.Exact.mono_gproof · cited by 10
- CategoryTheory.ShortComplex.exact_iff_epiproof · cited by 8
- CategoryTheory.Limits.biprod.lift_descproof · cited by 7
- CategoryTheory.Limits.zero_of_epi_compproof · cited by 7
- CategoryTheory.Limits.zero_of_source_iso_zeroproof · cited by 7
Showing the 200 most cited of 367.