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For questions about coalgebras, comultiplication, cocommutativity, counity, comodules, bicomodules, coactions, corepresentations, cotensor product, subcoalgebras, coideals, coradical, cosemisimplicity, ...

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Coradical filtration for comodules is exhaustive

Exhaustiveness of the coradical filtration of a coalgebra is proven in Theorem 5.2.2 of Montgomery's book "Hopf algebras and their actions on rings." This is not as general as what you asked for, sinc …
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