A Type B Analogue of the Category of Finite Sets with Surjections

We define a type B analogue of the category finite sets with surjections, and we study representation theory this category. show that opposite is quasi-Gröbner, which implies submodules finitely generated modules are again generated. prove generating functions have certain prescribed poles, obtain restrictions on representations Coxeter groups can appear in such modules. Our main example module categorifies degree i Kazhdan–Lusztig coefficients arrangements.