List questions from homological-algebra

Published on 26 Mar 2026 - 6:34

73

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Adjunction of the full embedding $E$ From $ _{R} Free$ to $_{R } Mod$, where $_{R}$Free is the category of free left modules.

Published on 29 Mar 2026 - 19:36

172

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A ring homomorphism $f:R \to S$ induce a ring homomorphism $H^(X,A;R)\to H^(X,A;S)$ on cohomology rings

Published on 25 Dec 2019 - 22:07

158

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Does $\text{Tor}_1^R(M, M) = M$?

Published on 25 Mar 2026 - 12:31

65

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Cohomology of a complex included in a big commutative diagram

Published on 27 Dec 2019 - 13:08

81

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$C_n(X;G)$ is naturally isomorphic to $C_n(X) \otimes G$

Published on 25 Mar 2026 - 12:20

548

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Understanding proof that $\operatorname{Ext}^1(P, M)=0\; \forall M$ implies $P$ is projective

Published on 30 Mar 2026 - 17:38

123

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Rotman's Homological Algebra Text, Def of Adjoint Functors

Published on 30 Dec 2019 - 23:44

362

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a categorical proof for split short exact sequences

Published on 26 Mar 2026 - 22:19

52

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If $f \colon K \rightarrow L$ be a chain equivalence then $H_n (f) \colon H_n (K) \rightarrow H_n (L)$ is an isomorphism

Published on 01 Jan 2020 - 11:55

53

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Existence of a chain map

Published on 25 Mar 2026 - 6:00

244

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Short Exact Sequences as Fiber Bundles

Published on 26 Mar 2026 - 17:12

551

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Hatcher n-Torus Cohomology

Published on 03 Jan 2020 - 18:39

300

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Why this s.e.s. splits?

Published on 26 Mar 2026 - 6:18

81

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The associator is a cocycle

Published on 04 Jan 2020 - 17:39

List Question

Ext groups of sheaves and sheaf cohomology in the context of duality theorems

Adjunction of the full embedding $E$ From $ _{R} Free$ to $_{R } Mod$, where $_{R}$Free is the category of free left modules.

A ring homomorphism $f:R \to S$ induce a ring homomorphism $H^(X,A;R)\to H^(X,A;S)$ on cohomology rings

Does $\text{Tor}_1^R(M, M) = M$?

Cohomology of a complex included in a big commutative diagram

$C_n(X;G)$ is naturally isomorphic to $C_n(X) \otimes G$

Understanding proof that $\operatorname{Ext}^1(P, M)=0\; \forall M$ implies $P$ is projective

Rotman's Homological Algebra Text, Def of Adjoint Functors

a categorical proof for split short exact sequences

If $f \colon K \rightarrow L$ be a chain equivalence then $H_n (f) \colon H_n (K) \rightarrow H_n (L)$ is an isomorphism

Existence of a chain map

Short Exact Sequences as Fiber Bundles

Hatcher n-Torus Cohomology

Why this s.e.s. splits?

The associator is a cocycle

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