The geometry of self-adjunction

Abstract

This paper is a companion to another paper where it is shown that the multiplicative monoids of Temperley-Lieb algebras are isomorphic to monoids of endomorphisms in categories where en endofunctor is adjoint to itself. Such a self-adjunction underlines the orthogonal group case of Baruer's representation of the Baruer centralizer algebras. The present paper provides detailed proofs of results on the presentation of various monoids of diagrams by generators and relations, on which the other paper depends.