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Results tagged with homological-algebra
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user 2503
(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.
3
votes
1
answer
176
views
Coinciding induced maps
Of course if two morphisms of complexes are homotopic their induced maps coincide, but I'm wondering about the converse: if the induced maps on the cohomologies coincide, when does that imply that the …
- 5,901
10
votes
1
answer
9k
views
Examples of computing Ext and Tor functors?
So I understand in theory the definition of Ext and Tor, but when it comes to actually computing them, I'm stuck. For example, could someone show me how to compute $\text{Ext}(\mathbb{Z}/m\mathbb{Z}, …
- 5,901
6
votes
Accepted
Do $RHom(C,D)$ and $DG(C,D)$ have equivalent homotopy categories?
Toen proved that $RHom$ provides the internal hom in the homotopy category of dg-categories. For what you want to be true, you need something more than this: you need to know that $RHom$ is actually …
- 5,901