List questions from homological-algebra

Published on 26 Mar 2026 - 6:30

178

Views

Is $R\operatorname{Hom}(\bullet,R)$ a triangulated functor? What is the opposite of a triangulated category?

Published on 29 Mar 2026 - 16:50

57

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Two definitions of the differential are equal

Published on 02 Jun 2020 - 7:57

80

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Deriving spectral sequence of a filtered complex

Published on 25 Mar 2026 - 19:24

168

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Depth of $R/I$ as an $R$-module versus as a ring

Published on 03 Jun 2020 - 7:18

55

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converse of left exactness

Published on 03 Jun 2020 - 8:56

121

Views

Cyclic cohomology of a field $k$

Published on 25 Mar 2026 - 12:54

1.2k

Views

Ext and Tor duality

Published on 03 Jun 2020 - 17:18

127

Views

Depth of $i$-th syzygy module, where $i$ is at most the depth of the ring

Published on 04 Jun 2020 - 0:41

145

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$f:M \to Q$ a monomorphism with $Q$ injective and $g:M \to N$ an essential morphism, then there exists a mono $\bar{g}: N \to Q$ such $\bar{g} g= f$.

Published on 26 Mar 2026 - 14:30

186

Views

Finitely generated modules, Jacobson radical

Published on 27 Mar 2026 - 15:35

135

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Proving a subclass of modules is closed under extensions using some categorical properties.

Published on 05 Jun 2020 - 18:48

87

Views

Does Hom commute with mapping cone?

Published on 05 Jun 2020 - 21:41

338

Views

Proving $Ext_{\mathbb{Z}}^1(A,B)$ is a torsion-free abelian group, given that $A$ is divisible and $B$ is torsion-free

Published on 31 Mar 2026 - 11:36

290

Views

When is it enough to consider roofs in the derived category?

Published on 03 Apr 2026 - 14:44

List Question

Is $\frac{\bigcap_{k=1}^\infty M_k}{\bigcup_{k=1}^\infty N_k}$ a direct limit?

Is $R\operatorname{Hom}(\bullet,R)$ a triangulated functor? What is the opposite of a triangulated category?

Two definitions of the differential are equal

Deriving spectral sequence of a filtered complex

Depth of $R/I$ as an $R$-module versus as a ring

converse of left exactness

Cyclic cohomology of a field $k$

Ext and Tor duality

Depth of $i$-th syzygy module, where $i$ is at most the depth of the ring

$f:M \to Q$ a monomorphism with $Q$ injective and $g:M \to N$ an essential morphism, then there exists a mono $\bar{g}: N \to Q$ such $\bar{g} g= f$.

Finitely generated modules, Jacobson radical

Proving a subclass of modules is closed under extensions using some categorical properties.

Does Hom commute with mapping cone?

Proving $Ext_{\mathbb{Z}}^1(A,B)$ is a torsion-free abelian group, given that $A$ is divisible and $B$ is torsion-free

When is it enough to consider roofs in the derived category?

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