Theorems · Theorem · category theory
CategoryTheory.Limits.zero_comp
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] {X Y Z : C}
{f : Y ⟶ Z}, CategoryTheory.CategoryStruct.comp 0 f = 0- Cited by
- 339 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.zero_compproof · cited by 2
Cited by340
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.cokernelIsCokernelstatement · cited by 23
- CategoryTheory.Pretriangulated.Triangle.coyoneda_exact₂proof · cited by 16
- CategoryTheory.ShortComplex.toCycles_comp_homologyπproof · cited by 12
- CochainComplex.HomComplex.δ_shapeproof · cited by 11
- CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₁₂proof · cited by 11
- CategoryTheory.Limits.CokernelCofork.conditionproof · cited by 10
- CategoryTheory.ShortComplex.exact_iff_monoproof · cited by 8
- HomologicalComplex₂.d₁_eq_zeroproof · cited by 8
- HomologicalComplex₂.d₂_eq_zeroproof · cited by 8
Showing the 200 most cited of 340.