List questions from homological-algebra

Published on 18 Jan 2020 - 17:58

143

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Two definitions for regular rings

Published on 27 Mar 2026 - 21:52

114

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If $\operatorname{Ext}^{1}_{\mathbf Z}(A, F) \cong 0$ for all free groups F, then A is free?

Published on 19 Jan 2020 - 9:48

304

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Categorical duals for finitely-generated projective modules

Published on 29 Mar 2026 - 8:14

155

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Why bar resolution is acyclic complex of $G$-homomorphisms?

Published on 20 Jan 2020 - 7:09

805

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Doubt over a proof about higher direct image functors in Hartshorne

Published on 25 Mar 2026 - 12:37

154

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Why the composition of two functors is a bifunctor？

Published on 21 Jan 2020 - 13:15

250

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A short exact sequence is pure

Published on 27 Mar 2026 - 0:02

289

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Show that for Abelian groups $G$ and $H, \bigl[K(G, n), K(H, n)\bigr] \cong \operatorname{Hom}(G, H).$

Published on 26 Mar 2026 - 19:20

268

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Five lemma diagram without the middle vertical map

Published on 24 Jan 2020 - 20:45

121

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Chain map factoring through 0 map on Homology

Published on 25 Jan 2020 - 1:19

58

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restriction maps of the constant presheaf are necessarily identity

Published on 29 Mar 2026 - 16:50

64

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Derived functor and natural transformation

Published on 25 Mar 2026 - 12:32

142

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Equivalence of two definitions of "projective dimension of a complex"

Published on 28 Jan 2020 - 13:23

241

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Is $\mathbb{Q}_p/\mathbb{Z}_p$ an injective $\mathbb{Z}_p$-module?

Published on 26 Mar 2026 - 6:10

List Question

Projective Resolution and Homology

Two definitions for regular rings

If $\operatorname{Ext}^{1}_{\mathbf Z}(A, F) \cong 0$ for all free groups F, then A is free?

Categorical duals for finitely-generated projective modules

Why bar resolution is acyclic complex of $G$-homomorphisms?

Doubt over a proof about higher direct image functors in Hartshorne

Why the composition of two functors is a bifunctor？

A short exact sequence is pure

Show that for Abelian groups $G$ and $H, \bigl[K(G, n), K(H, n)\bigr] \cong \operatorname{Hom}(G, H).$

Five lemma diagram without the middle vertical map

Chain map factoring through 0 map on Homology

restriction maps of the constant presheaf are necessarily identity

Derived functor and natural transformation

Equivalence of two definitions of "projective dimension of a complex"

Is $\mathbb{Q}_p/\mathbb{Z}_p$ an injective $\mathbb{Z}_p$-module?

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