What is the category of Set-models of the category of finite sets?

Question

Let $\mathbf{FSet}$ denote the category of finite sets.

If we consider $\mathbf{FSet}^\text{op}$ as a Lawvere theory, we recover the category $\mathbf{Set}$ of sets as its models. If, instead, we take as our theory $\mathbf{FSet}$ itself (this is not a Lawvere theory now I think, but it still is an algebraic theory), what is the category of models?

Answer 1

$\mathbf{Set}^\text{op}$ is equivalent (by taking power sets) to the category of complete, atomic Boolean algebras.

In particular, $\mathbf{FinSet}^\text{op}$ is equivalent to the category of finite boolean algebras.

nLab has a page on FinSet. (and also on CABAs)