  Let $X$ be an algebraic variety with Gorenstein singularities. We define the
notion of a wonderful resolution of singularities of $X$ by analogy with the
theory of wonderful compactifications of semi-simple linear algebraic groups.
We prove that if $X$ has rational singularities and has a wonderful resolution
of singularities, then $X$ admits a categorical crepant resolution of
singularities. As an immediate corollary, we get that all determinantal
varieties defined by the minors of a generic square/symmetric/skew-symmetric
matrix admit categorical crepant resolution of singularities.
  We also discuss notions of minimality for a categorical resolution of
singularities and we explore some links between minimality and crepancy for
such resolutions.
