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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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Homotopy colimit of a simplicial DGA
It seems to be well-known that the homotopy colimit of a simplicial chain complex (unbounded) can be computed by taking the totalization of the associated (half-plane) double complex. The totalization …