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Results tagged with coalgebras
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user 121009
For questions about coalgebras, comultiplication, cocommutativity, counity, comodules, bicomodules, coactions, corepresentations, cotensor product, subcoalgebras, coideals, coradical, cosemisimplicity, ...
3
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Inverse limit of chains of Eilenberg Mac Lane spaces
\to C_*(K(G_2,n);F) \to C_*(K(G_1,n);F) \ (*)$$
on chains with F-coeffients seen as inverse system of conilpotent coassociative dg-coalgebras over $F$
has inverse limit $C_*(K(G,n);F).$
Is there a left … induced model structure on the category of conilpotent coassociative dg-coalgebras over $F$ such that $C_*(K(G,n);F)$ is the homotopy inverse limit of the diagram $(*)$? …
- 1,361
5
votes
0
answers
112
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Conilpotent coalgebras as pushouts of trivial coalgebras
Question: Can one obtain $C$ by iterately taking pushouts of trivial coalgebras (= coalgebras with zero comultiplication)? … Especially, does $C$ belong to the full subcategory generated by trivial coalgebras under small colimits?
If not, can anyone give a counterexample? …
- 1,361
3
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0
answers
89
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Do chains send homotopy inverse limits of spaces to homotopy inverse limits of $E_\infty$-co...
The limit in the category of graded abelian hopf algebras over $ \mathbb{F}_p$ forgets to the limit in the category of graded cocommutative coalgebras over $\mathbb{F}_p$ but does generally not forget … limit in graded cocommutative coalgebras over $\mathbb{F}_p$. …
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4
votes
0
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168
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Building conilpotent coalgebras from co-square-zero-extensions
We think of the $\mathrm{E}(\mathrm{X})$ as the most basic
conilpotent cocommutative non-counital dg-coalgebras. … implicitely use that the model structure on chain complexes over $\mathrm{K}$ with weak equivalences the quasi-isos lifts to a model structure on the category of conilpotent cocommutative non-counital dg-coalgebras …
- 1,361
5
votes
1
answer
433
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Tensor product of coaugmented conilpotent coalgebras
But taking the cokernel of the coaugmentation only defines an oplax symmetric monoidal functor from cocommutative coaugmented counital dg-coalgebras to cocommutative non-counital dg-coalgebras. … as monoids in the category of conilpotent cocommutative coaugmented counital dg-coalgebras. …
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