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

Wonderful resolutions and categorical crepant resolutions of singularities