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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.
5
votes
Elementary $\mathrm{Ext}^1$ intuition
I think this question is a great example of how intuition and the ability to compute go hand in hand. Thanks for asking! Say we have modules M and N. Here `to have' means to have a presentation as …