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Results tagged with homological-algebra
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user 31233
(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.
13
votes
Do pretopoi have cohomology and homotopy groups?
Already elementary toposes can fail to have enough injectives: Let $M$ be the model of ZF by Andreas Blass in his 1979 paper Injectivity, Projectivity, and the Axiom of Choice. The category of $M$-set …
- 3,312
6
votes
1
answer
377
views
Elementary proof of the exactness of Čech complex associated to a hypercovering ("Illusie's ...
Let $\mathcal{E}$ be a sheaf of abelian groups on a topological space (or a site). For an open covering $\mathfrak{U} = (U_i)_i$, it is well known that the augmented Čech complex $0 \to \mathcal{E} \t …
- 40.2k