Theorems · Definition · category theory
AlgebraicTopology.inclusionOfMooreComplexMap
{A : Type u_2} →
[inst : CategoryTheory.Category.{v_2, u_2} A] →
[inst_1 : CategoryTheory.Abelian A] →
(X : CategoryTheory.SimplicialObject A) →
(AlgebraicTopology.normalizedMooreComplex A).obj X ⟶ (AlgebraicTopology.alternatingFaceMapComplex A).obj XThe inclusion map of the Moore complex in the alternating face map complex
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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 · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- Oppositestatement · cited by 8,081
- SimplexCategorystatement · cited by 2,204
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- ComplexShape.downstatement · cited by 605
- CategoryTheory.SimplicialObjectstatement and proof · cited by 548
- ChainComplexstatement · cited by 350
- CategoryTheory.Subobject.arrowproof · cited by 175
- AlgebraicTopology.alternatingFaceMapComplexstatement · cited by 25
- AlgebraicTopology.normalizedMooreComplexstatement · cited by 14
Cited by14
Results whose statement or proof uses this declaration.
- AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMapstatement and proof · cited by 2
- AlgebraicTopology.DoldKan.N₁_iso_normalizedMooreComplex_comp_toKaroubiproof · cited by 2
- AlgebraicTopology.DoldKan.inclusionOfMooreComplexMap_comp_PInftystatement and proof · cited by 1
- AlgebraicTopology.DoldKan.HigherFacesVanish.inclusionOfMooreComplexMapstatement · cited by 1
- AlgebraicTopology.inclusionOfMooreComplexMap_fstatement · cited by 1
- AlgebraicTopology.inclusionOfMooreComplexproof · cited by 1
- AlgebraicTopology.DoldKan.inclusionOfMooreComplexMap_comp_PInfty_assocstatement and proof · cited by 0
- AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap_assocstatement and proof · cited by 0