List questions from homological-algebra

Published on 12 Apr 2026 - 16:13

109

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$\operatorname{Hom}_R(R/fR,X)$ is an exact functor

Published on 16 Apr 2026 - 10:32

629

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Compute homology groups using Mayer-Vietoris sequence

Published on 13 Apr 2026 - 6:42

213

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$H^n(G,U(1))= H^{n+1}(G,\mathbb{Z})$ only correct for finite group $G$? Universal coefficient theorem

Published on 10 May 2026 - 17:15

1.1k

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Categorical proof of direct sum preserving exactness

Published on 13 Apr 2026 - 17:28

156

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$\operatorname{Tor}^A_1(A/\mathfrak a,N) = 0$?

Published on 15 Apr 2026 - 6:12

471

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Homology group of $\mathbb{S}^1 \vee \mathbb{RP}^2$ and covering spaces

Published on 10 May 2026 - 17:42

317

Views

Clarification of Theorem 2.4.3 in Weibel (left derived functors are universal $\delta$-functors)

Published on 15 Apr 2026 - 22:42

342

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Why are there not $4$ kinds of derived functors/

Published on 12 Apr 2026 - 9:07

813

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Showing that a group ring is isomorphic to a tensor product

Published on 14 Apr 2026 - 10:26

55

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Short Exact Sequence proof confusion

Published on 15 Apr 2026 - 23:54

120

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$X$ and $Y$ same homotopy type, then isomorphism $H_n(X) \approx H_n(Y)$

Published on 14 Apr 2026 - 22:33

212

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Prelude to Rotman's proof of the Hurewicz Theorem

Published on 11 Apr 2026 - 10:24

941

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Existence of injective resolutions

Published on 10 Apr 2026 - 19:05

178

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Is Artinian algebra with finite injective dimension of itself is self-injective？

Published on 10 May 2026 - 16:34

List Question

Lift of chain complex diagram with acyclicity

$\operatorname{Hom}_R(R/fR,X)$ is an exact functor

Compute homology groups using Mayer-Vietoris sequence

$H^n(G,U(1))= H^{n+1}(G,\mathbb{Z})$ only correct for finite group $G$? Universal coefficient theorem

Categorical proof of direct sum preserving exactness

$\operatorname{Tor}^A_1(A/\mathfrak a,N) = 0$?

Homology group of $\mathbb{S}^1 \vee \mathbb{RP}^2$ and covering spaces

Clarification of Theorem 2.4.3 in Weibel (left derived functors are universal $\delta$-functors)

Why are there not $4$ kinds of derived functors/

Showing that a group ring is isomorphic to a tensor product

Short Exact Sequence proof confusion

$X$ and $Y$ same homotopy type, then isomorphism $H_n(X) \approx H_n(Y)$

Prelude to Rotman's proof of the Hurewicz Theorem

Existence of injective resolutions

Is Artinian algebra with finite injective dimension of itself is self-injective？

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