Let and be coalgebras.
Definition. Linear map is called coalgebra homomorphism if and .
If is a coalgebra and is a coideal, then we have canonical coalgebra structur on (please, see this entry (http://planetmath.org/SubcoalgebrasAndCoideals) for more details). Then the projection is a coalgebra homomorphism. Furthermore, one can show that the canonical coalgebra structure on is a unique coalgebra structure such that is a coalgebra homomorphism.
|Date of creation||2013-03-22 18:49:25|
|Last modified on||2013-03-22 18:49:25|
|Last modified by||joking (16130)|