[[Internalization]]
# Magma object

Let $(\cat C, \otimes, \mathbb{1}, \alpha, \lambda, \rho)$ be a [[monoidal category]].
A **magma** in $\cat C$ consists of the data #m/def/cat
$$
\begin{align*}
M \otimes M \xrightarrow m M
\end{align*}
$$
where $m$ is called **multiplication**.

## Examples

- A magma in [[Category of vector spaces]] is a [[K-algebra]].
- More generally for commutative $R$, a magma in [[Category of modules over a commutative ring|$\lMod R$]] is an [[R-algebra]].
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