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Another isomorphism of categories arises in the theory of Boolean algebras: the category of Boolean algebras is isomorphic to the category of Boolean rings.
Given a Boolean algebra B, we turn B into a Boolean ring by using the symmetric difference as addition and the meet operation as multiplication.
Conversely, given a Boolean ring R, we define the join operation by a ' b = a + b + ab, and the meet operation as multiplication.
Again, both of these assignments can be extended to morphisms to yield functors, and these functors are inverse to each other.

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