Linear algebra MOC

𝑅-comonoid

Let 𝑅 be a commutative ring. An 𝑅-comonoid 𝑇 is a comonoid in [[Category of modules over a commutative ring|𝑅𝖬𝗈𝖽]]. calg

Sweedler notation

It is convenient to introduce Sweedler notation, where we write

Δ𝑎=∑(𝑎)𝑎(1)⊗𝑎(2).

The idea is that the tensor Δ𝑎 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

---

develop | en | SemBr