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Generalization of Linear Morphisms on N in Topoi

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The definition of linear morphisms is generalized to the natural number object. Properties of such morphisms are investigated. The necessary and sufficient condition of monocity of a linear morphism of an arbitrary topos is formulated. Linear monomorphisms are demonstrated to be split. Two proofs of complementarity and, accordingly, decidability of linear monomorphisms are proposed.

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  1. Colin McLarty, “Learning from questions on categorical foundations,” Philosophia Mathematica (3), No. 13, 44–60 (2005).

  2. S. Mac Lane, Categories for the Working Mathematician [Russian translation], Fizmatlit, Moscow (2004).

    Google Scholar 

  3. A. I. Provotar, “Linear morphisms in a topos,” Kibern. Sist. Anal., No. 2, 3–10 (1997).

  4. P. Lietz, “From constructive mathematics to computable analysis via the realizability interpretation,” PhD thesis, Technischen Universitat, Darmstadt (2004).

    Google Scholar 

  5. A. I. Chentsov and A. I. Provotar, “Finite Cartesian products of natural number objects in topoi,” Computer Mathematics, No. 2, 136–143 (2004).

  6. R. Goldblatt, Topoi: The Categorical Analysis of Logic [Russian translation], Mir, Moscow (1983).

    Google Scholar 

  7. P. T. Johnstone, Topos Theory [Russian translation], Nauka, Moscow (1986).

    Google Scholar 

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Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 66–72, September–October 2005.

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Chentsov, A.I., Provotar, A.I. Generalization of Linear Morphisms on N in Topoi. Cybern Syst Anal 41, 688–694 (2005).

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