singularChainComplexFunctor — Mathlib

English

The singular chain complex functor with coefficients in C is a functor from C to the functor category SSet ⥤ ChainComplex C ℕ.

Русский

Сурр singular chain complex functor с коэффициентами в C есть функтор от C к функторной категории SSet ⥤ ChainComplex C ℕ.

LaTeX

$$$$ \mathrm{singularChainComplexFunctor} : C \to \big(\mathrm{SSet} \to \mathrm{ChainComplex} C \mathbb{N} \big) $$$$

Lean4

/-- The singular chain complex associated to a simplicial set, with coefficients in `X : C`.
One can recover the ordinary singular chain complex when `C := Ab` and `X := ℤ`.
-/
def singularChainComplexFunctor : C ⥤ SSet.{w} ⥤ ChainComplex C ℕ :=
  (Functor.postcompose₂.obj (AlgebraicTopology.alternatingFaceMapComplex _)).obj
    (sigmaConst ⋙ SimplicialObject.whiskering _ _)

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