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On the 3-arrow calculus for homotopy categories. (English) Zbl 1218.18011
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.
18G55 Nonabelian homotopical algebra (MSC2010)
55U35 Abstract and axiomatic homotopy theory in algebraic topology
18E35 Localization of categories, calculus of fractions
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