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3 votes

Semidirect products and PROPs

Dear Dan, You can find this notion defined in the paper "Framed discs operads and the equivariant recognition principle" by Nathalie Wahl and Paolo Salvatore: http://arxiv.org/abs/math/0106242 . . …
Bruno V.'s user avatar
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6 votes
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Is the operadic butterfly symmetric?

I have never seen such a functor and I doubt that it would exist. For instance, the operad Com is symmetric and one-dimensional in every arity. Whereas the operad Dend is regular (coming from a non-sy …
Bruno V.'s user avatar
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7 votes
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Model structure for cooperads and for coalgebras

Question 1. I do not know precisely. But here are some references that address the question of model category structures on cooperads and coalgebras over a cooperads. Aubry—Chataur « Cooperads and c …
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15 votes

Higher homotopy algebraic structure on the homology of an operad

To get the statement on the level of operads, remove the two first letters in the word "properad" and consider only rooted trees instead of graphs in loc. cit. … In the paper with Merkulov, we use the homotopy transfer theorem for co(pr)operads to understand the minimal model of the properad encoding associative bialgebras (we apply it to the bar construction). …
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