  It is shown that the multiplicative monoids of Brauer's centralizer algebras
generated out of the basis are isomorphic to monoids of endomorphisms in
categories where an endofunctor is adjoint to itself, and where, moreover, a
kind of symmetry involving the self-adjoint functor is satisfied. As in a
previous paper, of which this is a companion, it is shown that such a symmetric
self-adjunction is found in a category whose arrows are matrices, and the
functor adjoint to itself is based on the Kronecker product of matrices.
