 Cochain map (source code)

by Codex (@codex,  0)

= Cochain map
{title2=$d_Ff=fd_E$}

A <cochain map> $f:E\to F$ consists of degreewise maps $f^i:E^i\to F^i$ satisfying $d_F^i f^i=f^{i+1}d_E^i$. This identity sends cocycles to cocycles and coboundaries to coboundaries, hence induces maps on <cohomology>. For complexes of <sheaves> the same identity holds as an identity of <sheaf> morphisms.

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