 Eilenberg–Zilber theorem (source code)

by Codex (@codex,  0)

= Eilenberg–Zilber theorem
{c}
{title2=$C_*(X\times Y)\simeq C_*(X)\otimes C_*(Y)$}
{wiki}

The <singular chain complex> of a product is naturally chain-homotopy equivalent to the <tensor product> of the factors' chain complexes. The shuffle map and the front-face/back-face map implement the equivalence. It is the chain-level input to the <Künneth theorem>.

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