2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143170Guided by consideration of problems in 2 and 3 dimensional lattice model computation, we are led to define a number of new categories, and functors between these categories and the partition category, culminating in the introduction of two categories generalising the Temperley-Lieb category. We show how to compute practically in these categories, by giving a combinatorial realisation of their (topological) construction.48 pages, 20 figuresMathematical Physics81R50; 82B20text