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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.
2
votes
Classification of algebras of finite global dimension via determinants of certain 0-1-matrices
(Not a solution, just a reformulation and a conjecture for $w=3$)
(1) Remark: the question above may equivalently be stated as follows:
Let $Z$ be the matrix of the cyclic shift (the companion matri …