[[Linear algebra MOC]]
# $R$-comonoid

Let $R$ be a commutative ring.
An **$R$-comonoid** $T$ is a [[Comonoid object|comonoid]] in [[Category of modules over a commutative ring|$\lMod{R}$]]. #m/def/calg

## Sweedler notation

It is convenient to introduce **Sweedler notation**, where we write
$$
\begin{align*}
\Delta a = \sum_{(a)}a_{(1)} \otimes a_{(2)}.
\end{align*}
$$
The idea is that the tensor $\Delta a$ may be decomposed into a finite sum of separable tensors,
so we feel free to invoke such a decomposition without fixing it explicitly.

## Examples

- [[Free R-comonoid]]

## See also

- [[R-monoid|$R$-monoid]]
- [[Biunital biassociative bialgebra over a commutative ring]]

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