Tensor product of chain complexes
= Tensor product of chain complexes
{title2=$(C\otimes C')_k=\bigoplus_{p+q=k}C_p\otimes C'_q$}
= Tensor chain complex
{synonym}
The <tensor product> of homologically graded <chain complexes> has differential $D(x_p\otimes y)=dx_p\otimes y+(-1)^p x_p\otimes dy$. The sign makes the two mixed terms in $D^2$ cancel. Total degree is the sum of the two degrees.