9 citations · 34 across the 31 of their papers we have counts for
31 papers
Weil Diffeology I: Classical Differential Geometry
Hirokazu Nishimura
Topos theory is a category-theoretic axiomatization of set theory. Model categories are a category-theoretical framework for abstract homotopy theory. They are complete and cocompl…
Higher-Dimensional general Jacobi identities I
Hirokazu Nishimura
It was shown by the author [International Journal of Theoretical Physics 36 (1997), 1099-1131] in synthetic differential geometry that what is called the general Jacobi identity ob…
Synthetic differential geometry within homotopy type theory I
Hirokazu Nishimura
This paper gives a first step towards developing synthetic differential geometry within homotopy type theory. Its model theory will be discussed in a subsequent paper.
Synthetic Differential Geometry of Chen's Iterated Integrals
Hirokazu Nishimura
Chen's iterated integrals are treated within synthetic differential geometry. The main result is that iterated integrals produce a subcomplex of the de Rham complex on the free pat…
From the Biot-Savart Law to Ampere's Magnetic Circuital Law via Synthetic Differential Geometry
Hirokazu Nishimura
It is well known in classical electrodynamics that the magnetic field given by a current loop and the electric field caused by the corresponding dipoles in sheets are very similar,…
From Lie Algebras to Lie Groups within Synthetic Differential Geometry:Weil Sprouts of Lie's Third Fundamental Theorem
Hirokazu Nishimura
Weil prolongations of a Lie group are naturally Lie groups. It is not known in the theory of infinite-dimensional Lie groups how to construct a Lie group with a given Lie algebra a…