Mathlib Map

Theorems · Definition · category theory

AlgebraicTopology.AlternatingFaceMapComplex.obj

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] → CategoryTheory.SimplicialObject C → ChainComplex C ℕ

The alternating face map complex, on objects

Defined in
Mathlib.AlgebraicTopology.AlternatingFaceMapComplex
Cited by
146 results in Mathlib
Foundations
Depth 71 from the axioms, rests on 1,980 definitions · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Preadditive

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicTopology.DoldKan.PInfty · cited by 94DoldKan.PInftyAlgebraicTopology.DoldKan.N₁ · cited by 43DoldKan.N₁AlgebraicTopology.DoldKan.P · cited by 38DoldKan.PAlgebraicTopology.alternatingFaceMapComplex · cited by 25AlgebraicTopology.alterna…AlgebraicTopology.DoldKan.QInfty · cited by 20DoldKan.QInftyAlgebraicTopology.DoldKan.Q · cited by 18DoldKan.QAlgebraicTopology.DoldKan.Hσ · cited by 13DoldKan.HσAlgebraicTopology.DoldKan.hσ' · cited by 12DoldKan.hσ'AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex · cited by 10DoldKan.PInftyToNormalize…CategoryTheory.SimplicialObject.Splitting.toNondegComplex · cited by 9Splitting.toNondegComplexAlgebraicTopology.DoldKan.HigherFacesVanish.of_P · cited by 7HigherFacesVanish.of_PAlgebraicTopology.AlternatingFaceMapComplex.obj_d_eq · cited by 7AlternatingFaceMapComplex…AlgebraicTopology.DoldKan.PInfty_f_idem · cited by 7DoldKan.PInfty_f_idemCategoryTheory.SimplicialObject.Splitting.fromNondegComplex · cited by 7Splitting.fromNondegCompl…AlgebraicTopology.DoldKan.HigherFacesVanish.comp_P_eq_self · cited by 6HigherFacesVanish.comp_P_…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Preadditive · cited by 3309CategoryTheory.PreadditiveCategoryTheory.SimplicialObject · cited by 548CategoryTheory.Simplicial…ChainComplex · cited by 350ChainComplexAlgebraicTopology.AlternatingFaceMapComplex.objD · cited by 5AlternatingFaceMapComplex…ChainComplex.of · cited by 4ChainComplex.ofAlgebraicTopology.AlternatingFaceMapComplex.d_squared · cited by 1AlternatingFaceMapComplex…AlternatingFaceMapComplex.objCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by167

Results whose statement or proof uses this declaration.