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(Co)chain complexes, abelian Categories, (pre)sheaves, (co)homology in various (possibly highly generalized) settings, spectra, derived functors, resolutions, spectral sequences, homotopy categories. Chain complexes in an abelian category form the heart of homological algebra.
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Ding Gorenstein dimension
It is known that Gorenstein projective and Gorenstein injective dimensions of a ring R are equal. Is true also for ding projective and ding injective dimensions ?