symmetric monoidal (∞,1)-category of spectra
Given a natural number $n$, an n-ary operation on a set $S$ is a function
from the function set $\mathrm{Fin}(n) \to S$ to $S$ itself, where $\mathrm{Fin}(n)$ is the finite set with $n$ elements. The arity of the operation is $n$. In general, if the natural number $n$ is not specified, these are called finitary operations.
Sets with finitary operations are called finitary magmas or finitary groupoids.
More generally, a finitary operation in a multicategory is just a multimorphism.
More generally, one could use an arbitrary set instead of a finite set. However, the generalizations are only definable in closed multicategories, rather than any multicategory.
Every set $S$ with an $n$-ary operation $\phi$ comes with an endomorphism called the $n$-th power operation
where $S \overset{diag_n}{\longrightarrow} S^n$ is the diagonal morphism.
Last revised on December 9, 2022 at 17:23:36. See the history of this page for a list of all contributions to it.