  The $q$-Schur category is a $\mathbb{Z}[q,q^{-1}]$-linear monoidal category
closely related to the $q$-Schur algebra. We explain how to construct it from
the coordinate algebra of quantum $GL_n$ as $n \rightarrow \infty$. 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 $\mathbb{Z}[q,q^{-1}]$-form
for the $\mathfrak{gl}_n$-web category of Cautis, Kamnitzer and Morrison. We
also construct some explicit integral bases for morphism spaces in the latter
category.
