Theorems · Theorem · category theory
CategoryTheory.ShortComplex.cyclesMap_comp
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{S₁ S₂ S₃ : CategoryTheory.ShortComplex C} [inst_2 : S₁.HasLeftHomology] [inst_3 : S₂.HasLeftHomology]
[inst_4 : S₃.HasLeftHomology] (φ₁ : S₁ ⟶ S₂) (φ₂ : S₂ ⟶ S₃),
CategoryTheory.ShortComplex.cyclesMap (CategoryTheory.CategoryStruct.comp φ₁ φ₂) =
CategoryTheory.CategoryStruct.comp (CategoryTheory.ShortComplex.cyclesMap φ₁)
(CategoryTheory.ShortComplex.cyclesMap φ₂)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 36 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.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.ShortComplex.cyclesstatement · cited by 220
- CategoryTheory.ShortComplex.HasLeftHomologystatement and proof · cited by 132
- CategoryTheory.ShortComplex.leftHomologyDataproof · cited by 83
- CategoryTheory.ShortComplex.cyclesMapstatement · cited by 42
- CategoryTheory.ShortComplex.cyclesMap'_compproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- HomologicalComplex.cyclesMap_compproof · cited by 3
- CategoryTheory.ShortComplex.cyclesMap_comp_assocproof · cited by 0