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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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Confusion about signs in the definition of an $A_\infty$-algebra
We are trying to understand the definition of $A_\infty$-algebras. But we are puzzled by what appear to be two different sign conventions (and we cannot figure out how these two are equivalent)
We see …