著者

Nishimura Hirokazu

出版者

ELSEVIER

雑誌

Handbook of quantum logic and quantum structures : quantum logic

巻号頁・発行日

pp.227-260, 2007-08

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* single copies can be downloaded and printed for the reader's personal research and study

著者

Nishimura Hirokazu

巻号頁・発行日

pp.1-39, 2013-06-19

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After the torch of Anders Kock [Taylor series calculus for ring objects of line type, Journal of Pure and Applied Algebra, 12 (1978), 271-293], we will establish the Baker-Campbell-Hausdorff formula as well as the Zassenhaus formula in the theory of Lie groups.

著者

Nishimura Hirokazu

巻号頁・発行日

pp.1-21, 2013-06-09

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We refurbish our axiomatics of differential geometry introduced in [arXiv 1203.3911]. Then the notion of Euclideaness can naturally be formulated. The principal objective in this paper is to present an adaptation of our theory of differential forms developed in [International Journal of Pure and Applied Mathematics, 64 (2010), 85-102] to our present axiomatic framework.

著者

Nishimura Hirokazu

巻号頁・発行日

pp.1-18, 2012-12-05

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This paper is the sequel to our previous paper (Differetial Geometry ofMicrolinear Fr¨olicher spaces IV-1), where three approaches to jet bundlesare presented and compared. The first objective in this paper is to give theaffine bundle theorem for the second and third approaches to jet bundles.The second objective is to deal with the three approaches to jet bundles inthe context where coordinates are available. In this context all the threeapproaches are shown to be equivalent.

著者

Nishimura Hirokazu

巻号頁・発行日

pp.1-70, 2012-12-05

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The fourth paper of our series of papers entitled ”Differential Geometryof Microlinear Fr¨olicher Spaces is concerned with jet bundles. We presentthree distinct approaches together with transmogrifications of the firstinto the second and of the second to the third. The affine bundle theoremand the equivalence of the three approaches with coordinates are relegatedto a subsequent paper.

著者

Nishimura Hirokazu

巻号頁・発行日

pp.1-52, 2012-11-26

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In our previous paper (Axiomatic Differential Geometry II-3) we havediscussed the general Jacobi identity, from which the Jacobi identity ofvector fields follows readily. In this paper we derive Jacobi-like identitiesof tangent-vector-valued forms from the general Jacobi identity.

著者

Nishimura Hirokazu

巻号頁・発行日

pp.1-14, 2012-11-05

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In this paper we give an axiomatization of differential geometry comparable to model categories for homotopy theory. Weil functors play a predominant role.

著者

Nishimura Hirokazu

巻号頁・発行日

pp.1-52, 2012-10-28

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As the fourth paper of our series of papers concerned with axiomatic differential geometry, this paper is devoted to the general Jacobi identity supporting the Jacobi identity of vector fields. The general Jacobi identity can be regarded as one of the few fundamental results belonging properly to smootheology.

著者

Nishimura Hirokazu

巻号頁・発行日

pp.1-13, 2012-10-18

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The principal objective in this paer is to study the relationship between the old kingdom of differential geometry (the category of smooth manifolds) and its new kingdom (the category of functors on the category of Weil algebras to some smooth category). It is shown that the canonical embedding of the old kingdom into the new kingdom preserves Weil functors.

著者

Nishimura Hirokazu

巻号頁・発行日

pp.1-12, 2012-10-18

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Given a complete and (locally) cartesian closed category U, it is shown that the category of functors from the category of Weil algebras to the category U is (locally, resp.) cartesian closed. The corresponding axiomatization for differential geometry is then given.