  It is shown that the multiplicative monoids of Temperley-Lieb algebras
generated out of the basis are isomorphic to monoids of endomorphisms in
categories where an endofunctor is adjoint to itself. Such a 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. This self-adjunction
underlies the orthogonal group case of the Brauer representation of the Brauer
centralizer algebra.
