List questions from homological-algebra

Published on 26 Mar 2026 - 12:41

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Chain homotopy and projective complex

Published on 28 Mar 2026 - 4:52

137

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If $X=S^2$ and $A$ is a finite set of $k$ points in $X$, show $\tilde{H}_0(A)\simeq\mathbb{Z}^{k-1}$ and $\tilde{H}_i(A)=0$ for $i>0$.

Published on 02 Nov 2016 - 14:24

429

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On Poincaré duality and the universal coefficient theorem

Published on 25 Mar 2026 - 15:59

262

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Horseshoe lemma for Cartan-Eilenberg resolution

Published on 03 Nov 2016 - 8:54

255

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Is "generalized" singular homology/cohomology a thing? If not, why not?

Published on 29 Mar 2026 - 12:11

1k

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Local-Global Ext sequence

Published on 25 Mar 2026 - 22:25

808

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Why are all of these Ext's not zero?

Published on 25 Mar 2026 - 19:04

393

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Short exact sequence $0 \to A \to B \to C \to 0$ has invariant in $\text{Ext}^1(C,A)$

Published on 25 Mar 2026 - 16:02

1k

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Computing Tor using flat resolutions

Published on 06 Nov 2016 - 23:35

215

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Is $\mathbb{C}$ projective as a $\mathbb{C}[x,y]/(x^3,y^3,xy)$-module?

Published on 28 Mar 2026 - 6:48

736

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Classification of chain complexes of free abelian groups

Published on 07 Nov 2016 - 10:33

561

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A consequence of the Snake lemma

Published on 27 Mar 2026 - 21:34

316

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Isomorphism induced on homology

Published on 09 Nov 2016 - 16:51

1.3k

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Left adjoint to Hom(_,M)

Published on 26 Mar 2026 - 7:57

List Question

Check my working: how could $H_1^\Delta(T)=\mathbb{Z}_2$?

Chain homotopy and projective complex

If $X=S^2$ and $A$ is a finite set of $k$ points in $X$, show $\tilde{H}_0(A)\simeq\mathbb{Z}^{k-1}$ and $\tilde{H}_i(A)=0$ for $i>0$.

On Poincaré duality and the universal coefficient theorem

Horseshoe lemma for Cartan-Eilenberg resolution

Is "generalized" singular homology/cohomology a thing? If not, why not?

Local-Global Ext sequence

Why are all of these Ext's not zero?

Short exact sequence $0 \to A \to B \to C \to 0$ has invariant in $\text{Ext}^1(C,A)$

Computing Tor using flat resolutions

Is $\mathbb{C}$ projective as a $\mathbb{C}[x,y]/(x^3,y^3,xy)$-module?

Classification of chain complexes of free abelian groups

A consequence of the Snake lemma

Isomorphism induced on homology

Left adjoint to Hom(_,M)

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