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Results tagged with homological-algebra
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user 117693
(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.
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What properties do the categories $\mathbf{GrpMod}$ and $\mathbf{GrpMod}^*$ of compatible pa...
Consider the following category $\mathbf{GrpMod}^*$ of compatible pairs, that is:
an object is a pair $(G,M)$, where $G$ is a group and $M$ is a left $\Bbb Z[G]$-module. A morphism $(G,M) \to (H,N)$ i …
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1
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What properties do the categories $\mathbf{GrpMod}$ and $\mathbf{GrpMod}^*$ of compatible pa...
@Z.M pointed out in the comments that a useful framework to look into is animation. If we want a $1$-category to to have an animation, the natural question to ask is if is an algebraic category, which …
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What can be said about the derived functor of a composition between unbounded derived catego...
Let $\mathcal A, \mathcal B,\mathcal C$ be abelian categories and let $F:\mathcal A \to \mathcal B,G: \mathcal B \to \mathcal C$ be left exact functors such that $RF:D(\mathcal A) \to D(\mathcal B), R …
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