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Is singular homology a functor or a family?

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#algebraic-topology #homology-cohomology #homological-algebra
775
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Properties of injective modules

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#abstract-algebra #category-theory #homological-algebra #injective-module #algebraic-k-theory
358
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Simple applications of higher derived functors

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#soft-question #homological-algebra #big-list #applications #derived-functors
35
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Definition: Tower of Rings

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#ring-theory #homological-algebra
91
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Making a diagram commute

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#commutative-algebra #homological-algebra #diagram-chasing
259
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If $X$ is a $CW-$complex. Are $C_*(X)$ and $C^{CW}_*(X)$ weakly equivalent?

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#algebraic-topology #homological-algebra #cw-complexes
484
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Projective objects in functor categories

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#homological-algebra #abelian-categories
59
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The category of complexes modulo homotopy is triangulated

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#homological-algebra #derived-categories #triangulated-categories
108
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Example additive functor which is neither right exact nor left exact.

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#category-theory #homological-algebra #abelian-groups #abelian-categories
38
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Sequence of additive functors

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#category-theory #homological-algebra
1.8k
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Every $R$-module is projective if and only if every $R$-module is injective

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#abstract-algebra #modules #representation-theory #homological-algebra #solution-verification
153
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On the first Local Cohomology module of a complete local ring of depth $1$

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#commutative-algebra #homological-algebra #local-cohomology #primary-decomposition
61
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What is the colimit of this diagram of binary sequences?

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#algebraic-topology #category-theory #homological-algebra #limits-colimits
166
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Weibel IHA Exercise 1.2.4

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#homological-algebra
285
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Prove the dual of Schanuel's Lemma.

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#abstract-algebra #modules #homological-algebra

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