I will introduce the upper finite weakly triangular categories, which includes cyclotomic oriented Brauer categories, cyclotomic Brauer categories and cyclotomic Kauffman categories. Let A be the locally unital algebra associated to any upper finite weakly triangular category. We show that the category A-lfdmod of locally finite dimensional left A-modules is an upper finite fully stratified category in the sense of Brundan-Stroppel. As an application, we give details on the representations of cyclotomic Kauffman categories.  In this case, the subcategory of A-lfdmod in which each object admits a finite standard filtration can be used to categorify certain “integral highest modules” of certain Lie algebras. This talk is based on a joint work with M. Gao and L. Song

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