  Let $X$ be a quasi-compact, separated scheme over a field k and we can
consider the categorical resolution of singularities of $X$. In this paper let
$k^{\prime}/k$ be a field extension and we study the scalar extension of a
categorical resolution of singularities of $X$ and we show how it gives a
categorical resolution of the base change scheme $X_{k^{\prime}}$. Our
construction involves the scalar extension of derived categories of DG-modules
over a DG algebra. As an application we use the technique of scalar extension
developed in this paper to prove the non-existence of full exceptional
collections of categorical resolutions for a projective curve of genus $\geq 1$
over a non-algebraically closed field.
