The Lawvere theory of Boolean functions

Annoying Precision

Let $latex 2$ be a set with two elements. The category of Boolean functions is the category whose objects are the finite powers $latex 2^k, k in mathbb{Z}_{ge 0}$ of $latex 2$ and whose morphisms are all functions between these sets. For a computer scientist, the morphisms of this category have the interpretation of functions which input and output finite sequences of bits.

Since this category has finite products and is freely generated under finite products by a single object, namely $latex 2$, it is a Lawvere theory.

Question: What are models of this Lawvere theory?

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