Abstract
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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REFERENCES
Colin McLarty, “Learning from questions on categorical foundations,” Philosophia Mathematica (3), No. 13, 44–60 (2005).
S. Mac Lane, Categories for the Working Mathematician [Russian translation], Fizmatlit, Moscow (2004).
A. I. Provotar, “Linear morphisms in a topos,” Kibern. Sist. Anal., No. 2, 3–10 (1997).
P. Lietz, “From constructive mathematics to computable analysis via the realizability interpretation,” PhD thesis, Technischen Universitat, Darmstadt (2004).
A. I. Chentsov and A. I. Provotar, “Finite Cartesian products of natural number objects in topoi,” Computer Mathematics, No. 2, 136–143 (2004).
R. Goldblatt, Topoi: The Categorical Analysis of Logic [Russian translation], Mir, Moscow (1983).
P. T. Johnstone, Topos Theory [Russian translation], Nauka, Moscow (1986).
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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). https://doi.org/10.1007/s10559-006-0005-7
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DOI: https://doi.org/10.1007/s10559-006-0005-7