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The q-Schur category is a Zq, q^-1-linear monoidal category closely related to the q-Schur algebra. We explain how to construct it from the coordinate algebra of quantum GLₙ as n. Then we use Donkin's work on Ringel duality for q-Schur algebras to make precise the relationship between the q-Schur category and a Zq, q^-1-form for the glₙ-web category of Cautis, Kamnitzer and Morrison. We also construct some explicit integral bases for morphism spaces in the latter category.
Jonathan Brundan (Tue,) studied this question.