Theorems · Theorem · category theory
CategoryTheory.ShortComplex.p_opcyclesMap
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{S₁ S₂ : CategoryTheory.ShortComplex C} [inst_2 : S₁.HasRightHomology] [inst_3 : S₂.HasRightHomology] (φ : S₁ ⟶ S₂),
CategoryTheory.CategoryStruct.comp S₁.pOpcycles (CategoryTheory.ShortComplex.opcyclesMap φ) =
CategoryTheory.CategoryStruct.comp φ.τ₂ S₂.pOpcycles- Cited by
- 6 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.
Cites13
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.X₂statement · cited by 1,115
- CategoryTheory.ShortComplex.Hom.τ₂statement · cited by 243
- CategoryTheory.ShortComplex.opcyclesstatement · cited by 192
- CategoryTheory.ShortComplex.HasRightHomologystatement and proof · cited by 125
- CategoryTheory.ShortComplex.pOpcyclesstatement · cited by 84
- CategoryTheory.ShortComplex.rightHomologyDataproof · cited by 64
- CategoryTheory.ShortComplex.opcyclesMapstatement · cited by 41
Cited by6
Results whose statement or proof uses this declaration.
- HomologicalComplex.p_opcyclesMapproof · cited by 7
- CategoryTheory.ShortComplex.cyclesOpIso_inv_naturalityproof · cited by 3
- CategoryTheory.ShortComplex.π_homologyMap_ιproof · cited by 3
- CategoryTheory.ShortComplex.p_opcyclesMap_assocproof · cited by 3
- HomologicalComplex.pOpcycles_opcyclesIsoSc'_homproof · cited by 1
- HomologicalComplex.pOpcycles_opcyclesIsoSc'_invproof · cited by 1