Timeline for Is the cohomology of a topological operad a cooperad?
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| Feb 24, 2010 at 8:30 | comment | added | Pascal Lambrechts | You can also do tis in the category of graded algebra, so you get indeed a cooperad of algebras using the cup products. Notice however that if you do this in homology you get an operad of coalgebras (the coalgebra structure in homology is dual to the algebra structure of cohomology). Therefore you dot not really gain more structure passing from homology to cohomology. As Tilman pointed out homology is actually better when you deal with space of not finite type (whch is actually rare in the usual applications) | |
| Feb 23, 2010 at 14:52 | comment | added | skupers | You consider the symmetric monoidal category of graded vector spaces, thereby forgetting about the cup product. Does the statement fail if we use the category of algebras over $F$ with tensor product, trying to remember the cup product? | |
| Feb 22, 2010 at 20:39 | history | edited | Pascal Lambrechts | CC BY-SA 2.5 |
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| Feb 22, 2010 at 20:31 | history | edited | Pascal Lambrechts | CC BY-SA 2.5 |
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| Feb 22, 2010 at 20:14 | history | answered | Pascal Lambrechts | CC BY-SA 2.5 |