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Results tagged with coalgebras
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user 22131
For questions about coalgebras, comultiplication, cocommutativity, counity, comodules, bicomodules, coactions, corepresentations, cotensor product, subcoalgebras, coideals, coradical, cosemisimplicity, ...
3
votes
Is there a way to adjoin a counit to a non counital coalgebra?
Yes, it worked pretty much in the exact dual way: If $(C, \Delta)$ is a nonunital coalgebra, then $C \oplus k$ has a co-algebra structure given by:
$$ \Delta'(c + x)= \Delta(c) + c \otimes 1 + 1 \oti …
- 42.4k
9
votes
Accepted
presentability rank of categories of coalgebras
For the case of coalgebras, Jiří Rosický pointed out the key references to me by email:
The following theorem is due to Adámek and Porst in On tree coalgebras and coalgebra presentations as their Theorem … The category of $M$-coalgebras for a copointed endofunctor $M$ can be constructed as a full subcategory of the category of $M_0$-coalgebra where $M_0$ is the underlying endofunctor of $M$ as the equifier …
- 42.4k