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Titlebook: Calculus of Fractions and Homotopy Theory; Peter Gabriel,Michel Zisman Book 1967 Springer-Verlag Berlin · Heidelberg 1967 Calculus.Homotop

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https://doi.org/10.1007/0-8176-4459-8We will give here some applications of the preceding chapter to simplicial sets. We will also seize the opportunity to prove statements which will be used in the proof of the fundamental theorem of chapter VII.
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The Homotopic Category,Let . and . be simplicial sets, and let . (., . be the complex defined in II, 2.5.3. A vertex of. (., . is a morphism f: .→Z. If . and . are two vertices, a 1-simplex . of .(., . such that .= . and .. is a morphism .: ∆[1] × .→. which makes the following triangles commutative (Fig. 25).
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Exact Sequences of the Homotopic Category,We will give here some applications of the preceding chapter to simplicial sets. We will also seize the opportunity to prove statements which will be used in the proof of the fundamental theorem of chapter VII.
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