Search Results

Let $q$ be a prime and $q=p^r$ a power. Then there is a $p$-local fiber sequence from the $q-1$st stage of the James construction on $S^{2n}$, to $J(S^{2n}) = \Omega \Sigma S^{2n}$, to $J(S^{2nq}) = \ …

There is an operad whose algebras are objects with a homotopy unital multiplication -- the $A_2$ operad. There is an operad whose algebras are objects with a homotopy unital, homotopy associative obje …

Question: Is there a classification of $\mathcal V$-operads which are $\otimes_{BV}$-invertible? … That is, for which operads $O \in Op(\mathcal V)$ does there exist $P \in Op(\mathcal V)$ such that $O \otimes_{BV} P = Comm$? …

Question: For which operads $O$ does the statement For all cocartesian monoidal $D$, the forgetful functor $\operatorname{Alg}_O(D) \to D$ is an equivalence. hold? … And I'd be interested to understand the case of enriched operads as well. …

Certainly these operads are implicit in countless mathematical pursuits. …

On the other hand, these operads are Koszul dual (and perhaps the sign corresponds to the shift that appears in Koszul duality?). … More concretely, is it the case (under certain conditions, perhaps) that Koszul dual operads have inverse generating functions, up to some sign? …

The automorphism group $Aut(E_1)$ of the $E_1$ operad is the cyclic group of order 2, $C_2$, and thus $C_2$ acts on any category of algebras (by reversing the multiplication). The seeming coincidence …

The Lie operad is Koszul dual to the commutative operad. In some sense, the data of a formal group is an "elaboration" of the data of a Lie algebra. Is there some corresponding "elaboration" of the da …

Let $\mathcal C$ be a symmetric monoidal $\infty$-category, and let $O$ be an operad (for example, $O$ could be an $A_m$ or $E_n$ operad or a tensor product thereof, and $\mathcal C$ could be spaces o …