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Results tagged with homological-algebra
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user 6074
(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
Verdier duality under more general conditions
Let me add there is now a reference for the claims in Dan Peterson's answer, namely Marco Volpe has worked out the Topological $6$-functor formalism.
I also gave some (brief) account of this in Lectur …
- 21.3k
17
votes
Accepted
Yoga of six functors for group representations?
The accepted answer here is on a rather negative note -- I don't think that's fair! In fact, I think the correct answer is that all of this works, except that it is $\pi_\ast$ that gives group cohomol …
- 21.3k
8
votes
Accepted
periodic cyclic homology and tilting in the sense of Scholze
Of course, there cannot be a direct relation at the categorical level: After all, one category is $R$-linear while the other is $R^\flat$-linear (I write $R^\flat=R'$ for the tilt, as usual).
On the o …
- 21.3k
27
votes
What is homology anyway?
For a long time (and still today), I very much shared the confusion of the OP. I think Jacob Lurie gives a very clear take on the standard perspective, but Mike Shulman does have a very valid contrast …
- 21.3k