The q-Schur category is a Z[q,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 Z[q,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.
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Jonathan Brundan (2024) studied this question.
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