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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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Bimodule resolutions
I have asked this question on Mathematics Stack exachange but didn't get any reply yet. So, I am asking it here.
Let A be a finite-dimensional algebra. Let M be a left A-module and
N be a right A-mod …