Generalization of Linear Morphisms on N in Topoi
- 18 Downloads
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.
Keywordstopos linear morphism split monomorphism solvability
Unable to display preview. Download preview PDF.
- 1.Colin McLarty, “Learning from questions on categorical foundations,” Philosophia Mathematica (3), No. 13, 44–60 (2005).Google Scholar
- 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).Google Scholar
- 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).Google Scholar
- 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