There is the theory of containers (unrelated to the docker kind). They represent functors on sets and the differential operator on them satisfies the usual laws

There is the theory of containers (unrelated to the docker kind). They represent functors on sets and the differential operator on them satisfies the usual laws. In short a container is a set of shapes and a set of positions for data in each shape. The derivative of a container is the container you get by removing one position in each shape. An example of a container is the list container, which maps any set to the sets of lists of elements from the set. The derivative of the list is the pair of lists. As for multisets, the bag functor is better defined on groupoids than sets. But there is a generalised notion of container for groupoids, with a similar calculus. The bag functor is special because it is its own derivative, just like the exponential function.