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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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Generalizing Representation Theory of Finite Groups to Module Theory

My question is essentially this: which parts of the representation theory of finite groups are really just applications of module theory, and which are not? Here is an example of each case. Induction …
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