Sheaves, localizations, and unstable extensions: Some counterexamples (Q1175756)
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scientific article; zbMATH DE number 14461
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sheaves, localizations, and unstable extensions: Some counterexamples |
scientific article; zbMATH DE number 14461 |
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Sheaves, localizations, and unstable extensions: Some counterexamples (English)
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25 June 1992
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The author defines the notion of a universal closure operation for a locally presentable category \(\underline C\). However, a universal closure operation on \(\underline C\) need not be induced from a localization of \(\underline C\). The counterexample to prove this point occupies most of the paper. It is found by considering certain categories \(\mathbb{G}(M_ c)\) of groups over monoids and solving a suitable word problem. Using restricted categories the author also shows that sheafification need not preserve monics.
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universal closure operation
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locally presentable category
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categories of groups over monoids
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word problem
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sheafification
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