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We define a faithful linear monoidal functor from the partition category, andhence from Deligne's category $\mathrm{\underline{Re}p}(S_t)$, to theHeisenberg category. We show that the induced map on Grothendieck rings isinjective and corresponds to the Kronecker coproduct on symmetric functions.

Embedding Deligne's category $\mathrm{\underline{Re}p}(S_t)$ in the Heisenberg category