Quasi-hereditary twisted category algebras

We give a sufficient criterion for when a twisted finite category algebra over a field is quasi-hereditary, in terms of the partially ordered set of L-classes in the morphism set of the category. We show that this is a common generalisation of a long list of results in the context of EI-categories, regular monoids, Brauer algebras, Temperley–Lieb algebras, partition algebras.