Jellyfish Partition Categories
For each positive integer n , we introduce a monoidal category J P ( n ) $\mathcal {J}\mathcal {P}(n)$ using a generalization of partition diagrams. When the characteristic of the ground field is either 0 or at least n , we show J P ( n ) $\mathcal {J}\mathcal {P}(n)$ is monoidally equivalent to the full subcategory of Rep( A n ) whose objects are tensor powers of the natural n -dimensional permutation representation of the alternating group A n .