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Results tagged with coalgebras
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user 36146
For questions about coalgebras, comultiplication, cocommutativity, counity, comodules, bicomodules, coactions, corepresentations, cotensor product, subcoalgebras, coideals, coradical, cosemisimplicity, ...
12
votes
1
answer
898
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What are types of coalgebras that are more naturally described by cooperads?
But it seems to me that, in algebra at least, most notions of coalgebras encountered in nature are more naturally seen as coalgebras over operads, rather than coalgebras over cooperads. … over $\mathtt{P}$ and coalgebras over $\mathtt{P}^*$. …
- 5,040
4
votes
0
answers
327
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Is the bar construction of a CDGA model a Hopf algebra model for the loop space?
By a theorem of Adams, if $A = C^*(X;\mathbb{Q})$ is the CDGA of rational cochains on $X$ then the cohomology of the bar complex of $A$ is isomorphic to $H^*(\Omega X; \mathbb{Q})$ as a coalgebra (see …
- 5,040