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5 votes
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On a simple alternative correction to Roos' theorem on $\varprojlim^1$

Here is a discussion about an incorrect theorem of Roos, later corrected, some counterexamples and so on. Reading over this, I was a bit shocked because it contradicted something from Weibel's ...
FShrike's user avatar
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2 votes
0 answers
163 views

Coend of full subcategory

$\require{AMScd}$Let $F:\mathcal{C}^{op}\times \mathcal{C} \to \mathcal{D}$ be a functor and $\mathcal{C}' \subseteq \mathcal{C}$ a full subcategory. Assume that the coends $C$ over $F$ and $C'$ over $...
Bipolar Minds's user avatar
2 votes
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257 views

Why holim and not Rlim?

Let $\mathcal{A}$ be a Grothendieck category (I care mostly about modules over a ring). Let $\operatorname{Ch}^+(\mathcal{A})$ the category of bounded below cochain complexes, $\operatorname{D}^+(\...
Avi Steiner's user avatar
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1 vote
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54 views

contravariant finiteness and limit closure: is there dual to a result of Crawley-Boevey?

Let $\mathcal A$ be a locally finitely presented category. Theorem 4.2 of https://doi.org/10.1080/00927879408824927 says that given a full additive subcategory $\mathcal D$ of finitely presented ...
Alex's user avatar
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