The structure of a Jónsson-Tarski algebra can be described by an algebraic theory, with one binary operation $\mu$ and two unary operations $\lambda$ and $\rho$ such that $\mu(\lambda(x),\rho(x)) = x$, $\lambda(\mu(x,y))=x$, and $\rho(\mu(x,y))=y$.

The category of Jónsson-Tarski algebras is a topos, although this is not in general the case for algebraic theories. See here.

Revised on March 2, 2014 15:43:53
by Tim Campion?
(173.76.91.172)