symmetric monoidal (∞,1)-category of spectra
Given a natural number , an n-ary operation on a set is a function
from the function set to itself, where is the finite set with elements. The arity of the operation is . In general, if the natural number 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 with an -ary operation comes with an endomorphism called the -th power operation
where 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.