Hopf theory MOC

-comonoid

Let be a commutative ring. A -comonoid is a comonoid in , #m/def/ralg/hopf and thus consists of the data

satisfying the coünit law and the coässociative law.

Sweedler notation

It is convenient to introduce Sweedler notation, where we write

This extends to higher comultiplications, so that

The idea is that the tensor may be decomposed into a finite sum of separable tensors, so we feel free to invoke such a decomposition without fixing it explicitly.

Results

• Dual -monoid of a -comonoid

Examples

• Free -comonoid

See also

• -monoid
• Grouplike
• Coïdeal

#state/develop | #lang/en | #SemBr