On the 3-arrow calculus for homotopy categories (Q534532)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the 3-arrow calculus for homotopy categories |
scientific article |
Statements
On the 3-arrow calculus for homotopy categories (English)
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17 May 2011
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The author constructs a class of categories, called uni-fractionable categories, which have good localisations in the following sense: every morphism in the lcoalisation is represented by a zig-zag of length \(3\); two zig-zags represent the same morphism if and only if they can be embedded in a suitable \(3\times 3\) diagram. The axioms for a uni-fractionable category require the existence of certain factorisations, but they do not require these factorisations to be functorial. The result can be applied to arbitrary Quillen model categories.
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homotopy category
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localisation of categories
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3-arrow calculus
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derived category
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Quillen model category
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