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We study Gorenstein categories. We show that such a category has Tatecohomological functors and Avramov-Martsinkovsky exact sequences connecting theGorenstein relative, the absolute and the Tate cohomological functors. We showthat such a category has what Hovey calls an injective model structure and alsoa projective model structure in case the category has enough projectives. Asexamples we show that if X is a locally Gorenstein projective scheme then thecategory Qco(X) of quasi-coherent sheaves on $X$ is such a category and so hasthese features.

Gorenstein categories and Tate cohomology on projective schemes