A proxy-small geometric functor satisfies Grothendieck duality on all objects whose image is rigid, and the invertibility of its dualising object captures Matlis and Gorenstein duality.
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Duality in tensor-triangular geometry via proxy-smallness
A proxy-small geometric functor satisfies Grothendieck duality on all objects whose image is rigid, and the invertibility of its dualising object captures Matlis and Gorenstein duality.