Abstract: A fundamental question in modular representation theory is to find characters of simple modules for an algebraic group in prime characteristic. Lusztig conjectured that they could be computed via Kazhdan-Lusztig polynomials. However, Lusztig's conjecture was disproven in 2013 by Williamson. Instead, simple characters are expressed in terms of so-called p-Kazhdan-Lusztig polynomials, which are defined and computed at the categorical level. In this talk I will present the diagrammatic spherical category, which lends itself to such computations.