The paper I'm referring to can be found here. It came out in 2003. I've been told by professors before that I should be careful relying on things from this paper, because it contai …

Let \begin{equation} G := \biguplus_{p \geq 0} \: \biguplus_{q \geq 0} G(p, q) \end{equation} be a bigraded set of generators and $\mathcal{F}(G)$ be the free PRO generated by $G$ …

In Higher Operads, Higher Categories, Leinster nicely characterizes operads among monoidal categories (as PROs). Roughly speaking, a monoidal category comes from an operad if its s …

This question is closely related to my previous question about modules over truncated sphere spectra, in particular, it has the same motivation. Recall that every space (or ∞-grou …

The operadic butterfly is a diagram in the category of operads in vector spaces. It extends the short exact sequence relating commutative, associative and Lie operads. $$\begin{ar …

This question is motivated by the desire to understand better the interplay between Drinfeld associators, algebraic structures up to homotopy and related results. Recall that a Li …

Many different types of operads have emerged in recent years (symmetric, shuffle, cyclic, anticyclic, coloured, etc.). I would like, for any of these, list the following data: D …

Any symmetric operad can be considered as an non-$\Sigma$ operad by throwing away permutations. Does anyone know what sort of structure one gets for algebras over $C_n$ the little …

Ordinary operad with one ouput can be obviously regarded as free module on itself. Is there are analogous construction for operad with many outputs (PROP)? This must be difficult q …

Suppose I define a multicategory $M=(Ob(M),Hom_M)$ to be simply closed if for every sequence $S=(b_1,\ldots,b_n;x)$ of $n+1$ objects in $M$, we provide an object $Exp(S)\in Ob(M …

Is there a category of operads which allows morphisms which take operations to operations with more or fewer arguments? One example should be when you fix arguments to obtain maps …

Suppose I have an operad $P(n)$ in topological spaces in the sense of the book by Markl, Shnider and Stasheff, i.e. there is no space $P(0)$. In agreement with some of the answers …

First let $L^{\bullet}$ be a pro-nilpotent differential graded Lie algebra (dgla). We have the set of Maurer-Cartan elements in $L^{\bullet}$ ($MC(L^{\bullet})$) which are $\alpha …

I just discovered that something I've been working with has the structure of an operad. So I'm wondering what natural basic questions does one ask about operads? For example, if I …

Has anyone defined what it means for a modular operad to be Koszul, or what the Koszul dual of a modular operad is? In particular, is it meaningful to say that a modular operad is …