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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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