Theorems · Definition · category theory
ChainComplex.alternatingConst
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] → CategoryTheory.Functor C (ChainComplex C ℕ)The chain complex X ←0- X ←𝟙- X ←0- X ←𝟙- X ⋯.
It is exact away from 0 and has homology X at 0.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.Homproof · cited by 32,603
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- ComplexShape.downstatement and proof · cited by 605
- ComplexShape.Relproof · cited by 518
- ChainComplexstatement · cited by 350
- HomologicalComplex.alternatingConstproof · cited by 13
- ComplexShape.down_nat_odd_addproof · cited by 5
Cited by10
Results whose statement or proof uses this declaration.
- AlgebraicTopology.singularChainComplexFunctorIsoOfTotallyDisconnectedSpacestatement · cited by 1
- ChainComplex.alternatingConstHomologyDataEvenNEZerostatement and proof · cited by 1
- ChainComplex.alternatingConstHomologyDataOddstatement and proof · cited by 1
- ChainComplex.alternatingConst_exactAtstatement · cited by 1
- ChainComplex.alternatingConstHomologyDataZerostatement and proof · cited by 0
- ChainComplex.alternatingConstHomologyZerostatement · cited by 0
- ChainComplex.alternatingConstHomotopyEquivstatement · cited by 0
- ChainComplex.alternatingConst_map_fstatement and proof · cited by 0
- ChainComplex.alternatingConst_objstatement and proof · cited by 0
- AlgebraicTopology.alternatingFaceMapComplexConststatement · cited by 0