The Temperley–Lieb tower and the Weyl algebra

Abstract We define a monoidal category and a closely related 2‐category using diagrammatic methods. We show that acts on the category of modules over Temperley–Lieb algebras, with its generating 1‐morphisms acting by induction and restriction. The Grothendieck groups of and a third category we define are closely related to the Weyl algebra. We formulate a sense in which acts asymptotically on .