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Models for Lawvere theories are functors that preserve products. I'm a little confused about this detail: suppose you have a Lawvere theory for groups. If you have a specific group in mind, is there an obvious way to pick the functor so that it represents that group?

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AFAIK it just sends $1$ to the underlying set of a group, and $\pi: 1 \times 1 \to 1$ - to the group operation. – Alexei Averchenko Sep 3 '11 at 15:10
Ah that makes sense, I think that's the answer. – Joe Sep 3 '11 at 15:22

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