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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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Differentials on free algebras over operads
I am currently reading Cyclic Operads and Cyclic Homology by Getzler-Jones and have some confusions.
I am under the impression that given an (associative, say) algebra $A$ that an almost-free resoluti …