2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164588It 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.54 pages, minor correctionsGeometric Topology57M99, 20F36, 18A40text