Reference for the category of functors from finite sets with surjections to abelian groups

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In the talk of Jacob Lurie about Lie Algebras and Homotopy theory, he mention at the end about a category of functors that has the same derived category as the category as some category of universal Lie algebras.

I found a reference of the universal Lie Algebra, in the paper "The universal Lie algebra" of P. Vogel, but I cannot find a reference of this category of functors.

https://www.youtube.com/watch?v=LeaiPHAh0X0&t=1s