Theorems · Definition · algebraic topology
SSet.chainComplexMap
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.Limits.HasCoproducts C] →
[inst_2 : CategoryTheory.Preadditive C] → {X Y : SSet} → (X ⟶ Y) → (R : C) → X.chainComplex R ⟶ Y.chainComplex RThe morphism of simplicial chain complexes induces by a morphism of simplicial sets.
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 78 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.Functor.objproof · cited by 19,642
- CategoryTheory.Functor.mapproof · cited by 8,698
- Oppositestatement · cited by 8,081
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- SimplexCategorystatement · cited by 2,204
- SSetstatement and proof · cited by 1,283
- ComplexShape.downstatement · cited by 605
- ChainComplexstatement · cited by 350
- CategoryTheory.Limits.HasCoproductsstatement and proof · cited by 119
- SSet.chainComplexstatement · cited by 46
Cited by15
Results whose statement or proof uses this declaration.
- SSet.homologyMapproof · cited by 9
- SSet.normalizedChainComplexMapproof · cited by 5
- SSet.toNormalizedChainComplex_normalizedChainComplexMapstatement and proof · cited by 2
- SSet.chainComplexMap_PInftystatement · cited by 1
- CategoryTheory.SimplicialObject.Homotopy.sSetChainComplexMapstatement · cited by 1
- SSet.homologyMap_compproof · cited by 1
- SSet.Homotopy.chainComplexMapstatement · cited by 1
- SSet.ι_chainComplexMap_fstatement · cited by 1
- SSet.ι_chainComplexMap_f_assocstatement and proof · cited by 1
- SSet.ι_normalizedChainComplexMap_fproof · cited by 1
- SSet.toNormalizedChainComplex_normalizedChainComplexMap_assocstatement and proof · cited by 0
- SSet.chainComplexMap_PInfty_assocstatement and proof · cited by 0