Let be a monoid and a field. Consider the vector space over with basis . More precisely,
We identify with a function such that and for . Thus, every element in is of the form
for . The vector space can be turned into a -algebra, if we define multiplication as follows:
Furthermore, we can turn into a coalgebra as follows: comultiplication is defined by and counit is defined by . One can easily check that this defines coalgebra structure on .
|Date of creation||2013-03-22 18:58:48|
|Last modified on||2013-03-22 18:58:48|
|Last modified by||joking (16130)|