List questions from homological-algebra

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making an injective resolution for $A$.

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Contents of Tor modules

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If $\Gamma$ is $\Lambda$-projective and $C$ is $\Gamma$-injective, then $C$ is $\Lambda$-injective.

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How to compute $Ext_A^{1}(S_1, S_2)$ and $Ext_A^{1}(S_2, S_1)$?

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List Question

Does exactness in each variable coincide with exactness of the product?

Dependence of Euler characteristic on the coefficients

making an injective resolution for $A$.

Contents of Tor modules

Rank-nullity theorem for free $\mathbb Z$-modules

If $\Gamma$ is $\Lambda$-projective and $C$ is $\Gamma$-injective, then $C$ is $\Lambda$-injective.

How to compute $Ext_A^{1}(S_1, S_2)$ and $Ext_A^{1}(S_2, S_1)$?

Compatibility of homomorphisms and quotient maps of abelian groups

Spectral sequence of a filtered complex: convergence conditions and abelian categories

Construct natural transformation $u^* R^i f_* \rightarrow R^i g_* v^*$ without assumption of quasi-coherence

cohomology of suspension

Homology of $n$-sheeted covering space of Klein bottle

Quasi-isomorphism and homotopical equivalence

Converse of the Nine-Lemma (aka $ 3\times 3$ lemma)

Satellite functors in Cartan Eilenberg

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