coalgebra homomorphism
Let and be coalgebras.
Definition. Linear map is called coalgebra homomorphism if and .
Examples. Of course, if is a subcoalgebra of , then the inclusion is a coalgebra homomorphism. In particular, the identity is a coalgebra homomorphism.
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.
Title | coalgebra homomorphism |
---|---|
Canonical name | CoalgebraHomomorphism |
Date of creation | 2013-03-22 18:49:25 |
Last modified on | 2013-03-22 18:49:25 |
Owner | joking (16130) |
Last modified by | joking (16130) |
Numerical id | 4 |
Author | joking (16130) |
Entry type | Definition |
Classification | msc 16W30 |