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Results tagged with operads
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user 2811
9
votes
1
answer
356
views
Characterize algebras of the "topological simplices" operad
The operad of topological simplices, which I'll denote $\Delta$, has as $n$-ary operations the set
$$
\Delta_n:=\left\{P\colon\{1,\ldots,n\}\to[0,1]\;\middle|\;1=\sum_{i=1}^n P(i)\right\}
$$
of probab …
- 8,659
7
votes
1
answer
234
views
Monomorphisms in operad algebras
Setup: Let $\mathcal{O}$ be an operad in the category of sets, and let $\mathcal{O}\text{-Alg}$ denote the category of algebras on it (i.e., operad functors $\mathcal{O}\to\mathbf{Set}$. This category …
- 8,659
18
votes
1
answer
2k
views
Are Lurie's operads special SMCs?
In Higher Operads, Higher Categories, Leinster nicely characterizes operads among monoidal categories (as PROs). … But for the purposes of this question, all I need to say is that Leinster characterizes operads as special monoidal categories. Symmetric operads are again special symmetric monoidal categories. …
- 8,659
5
votes
2
answers
489
views
A (too?) simple notion of "closed multicategory"
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 $Exp(S)\in Ob(M)$, and
for every se …
- 8,659