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

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Radial Basis Function Networks,ollowing works:., P.: Catégories abéliennes. Bull. Soc. Math. France . (1962). ., A.: Sur quelques points d’algébre homologique. Tohoku math. J. serie 2. . (1957). ., S.: Homology. Berlin-Heidelberg-New York; Springer. ., B.: Theory of Categories. New York: Academic Press.

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Dictionary,ollowing works:., P.: Catégories abéliennes. Bull. Soc. Math. France . (1962). ., A.: Sur quelques points d’algébre homologique. Tohoku math. J. serie 2. . (1957). ., S.: Homology. Berlin-Heidelberg-New York; Springer. ., B.: Theory of Categories. New York: Academic Press.

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Neural Networks and Fuzzy SystemsA functor .: .→. is said make a morphism . of . invertible if . is invertible. We intend to associate with each category . and with each subset . of . . a category .[.] and a functor .: .→.[.] such that the following conditions are verified:

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Neural Networks and Fuzzy SystemsWe wish first to complete some results of the dictionary. Notations will be the same.

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Texture Recognition in Micromechanics,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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Neural Networks and MicromechanicsWe give here a unified account of some exact sequences which we meet in algebraic topology. The proofs we give do not modify in an essential way those of PUPPE. They are more abstract, selfdual and sometimes more simple (?).