« Dirichlet Product of Species

FinSet is closed under cartesian Products [00DZ]

FinSet is closed under cartesian products. Proof. See Notebook I.

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Definition. cartesian decomposition [00DQ]

Given a finite set , we define the type of cartesian decompositions by

Where cartesian product in FinSet.

Notation. [00E0]

For finite sets and , we write for finte set that is the cartesian product of and as constructed here.

By abuse of notation we will sometimes just write .