# Complex ** Matrix -- create the tensor product of a complex and a map of modules

## Synopsis

• Operator: **
• Usage:
h = C ** f
h = f ** C
• Inputs:
• C, , over a ring $R$
• f, , defining a homomorphism from the $R$-module $M$ to the $R$-module $N$
• Outputs:
• h, , from $C \otimes M$ to $C \otimes N$

## Description

For any chain complex $C$, a map $f \colon M \to N$ of $R$-modules induces a morphism $C \otimes f$ of chain complexes from $C \otimes M$ to $C \otimes N$. This method returns this map of chain complexes.

Tensoring with a complex defines a functor from the category of $R$-modules to the category of complexes over $R$.