singularChainComplexFunctorIsoOfTotallyDisconnectedSpace

English

Symmetry of little-o: if (f1 - f2) = o_l(g), then (f2 - f1) = o_l(g).

Русский

Симметрия нулевого типа: если (f1 - f2) = o_l(g), тогда (f2 - f1) = o_l(g).

LaTeX

$$ (f1 - f2) = o_l g \leftrightarrow (f2 - f1) = o_l g$$

Lean4

/-- If `X` is totally disconnected,
its singular chain complex is given by `R[X] ←0- R[X] ←𝟙- R[X] ←0- R[X] ⋯`,
where `R[X]` is the coproduct of copies of `R` indexed by elements of `X`. -/
noncomputable def singularChainComplexFunctorIsoOfTotallyDisconnectedSpace :
    ((singularChainComplexFunctor C).obj R).obj X ≅ (ChainComplex.alternatingConst.obj (∐ fun _ : X ↦ R)) :=
  (AlgebraicTopology.alternatingFaceMapComplex _).mapIso
      (((SimplicialObject.whiskering _ _).obj _).mapIso (TopCat.toSSetIsoConst X) ≪≫ Functor.constComp _ _ _) ≪≫
    AlgebraicTopology.alternatingFaceMapComplexConst.app _

Похожие утверждения