fundamental isomorphism theorem for coalgebras

Let (C,Δ,ε) and (D,Δ,ε) be coalgebras. Recall, that if D0D is a subcoalgebra, then (D0,Δ|D0,ε|D0) is a coalgebra. On the other hand, if IC is a coideal, then there is a canonical coalgebra structureMathworldPlanetmath on C/I (please, see this entry ( for more details).

Theorem. If f:CD is a coalgebra homomorphism, then ker(f) is a coideal, im(f) is a subcoalgebra and a mapping f:C/ker(f)im(f) defined by f(c+ker(f))=f(c) is a well defined coalgebra isomorphismPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath.

Title fundamental isomorphism theorem for coalgebras
Canonical name FundamentalIsomorphismTheoremForCoalgebras
Date of creation 2013-03-22 18:49:30
Last modified on 2013-03-22 18:49:30
Owner joking (16130)
Last modified by joking (16130)
Numerical id 4
Author joking (16130)
Entry type Theorem
Classification msc 16W30