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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.

6 votes
3 answers
1k views

Free Objects in Functor Categories

As a bit of background, consider the category of all covariant, additive functors from a small Abelian category $C$ to Abelian groups, which I'll denote $[C,Ab]$. First, $[C,Ab]$ is an Abelian catego …
Brian Hepler's user avatar
5 votes

How to visualize the Microsupport of a Sheaf?

This might be too late, or out-of-date for you, but I've always understood the microsupport best in terms of Morse theory (or microlocal Morse theory, or the stratified Morse theory of Goresky-MacPher …
Brian Hepler's user avatar