Combinatorial Structure

Let be a Ring containing .
Let be the Category of finite sets and bijections between them.
Let be the Category whose objects are pairs
where is a finite set and is a function
and Morphisms in are bijections
such that .

A combinatorial structure is a Functor
The map is called the weight function.
We may write just when the context is clear.

Often for all .
When weight is not specified, we assume that this is the case.