Dirichlet Series of Species [00EA]
Dirichlet Series of Species [00EA]
TODO 2. Identity Type of Dirichlet Type [00F6]
TODO 2. Identity Type of Dirichlet Type [00F6]
Idea 3. Generating Type of Species [00F8]
Idea 3. Generating Type of Species [00F8]
We can categorify the generating functions very similarly:
Notation 4. [00F0]
Notation 4. [00F0]
TODO 5. [00F4]
TODO 5. [00F4]
TODO 6. [00F5]
TODO 6. [00F5]
Definition 7. tame Species [00F2]
Definition 7. tame Species [00F2]
TODO
Definition 8. Dirichlet Species [00F3]
Definition 8. Dirichlet Species [00F3]
TODO
9. Dirichlet Series [00F1]
9. Dirichlet Series [00F1]
For a dirichlet species define
where is the dirichlet type of , and is the groupoid cardinality of the n-th component of the dirichlet type. We call the dirichlet series of , and the -th summand.
Definition 11. Dirichlet Product of functions [00FB]
Definition 11. Dirichlet Product of functions [00FB]
We can model the formal product of two dirichlet series by defining a dirichlet product for functions from into a ring, say .
For , define