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Models for Smooth Infinitesimal Analysis

Models for Smooth Infinitesimal Analysis,I. Moerdijk,G. E. Reyes

Models for Smooth Infinitesimal Analysis   (Citations: 99)
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Published in 1991.
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    • ...Note that there is a bijective correspondence between infinitesimal k-simplices and infinitesimal k-dimensional parallelepipeda in M. (Warning: the “infinitesimal singular rectangles” of [7], or the “marked microcubes” of [16], are in [15], and in [18] IV.1, called “infinitesimal k-cubes”; these things are not infinitesimal parallelepipeda in the sense of the present Definition...
    • ...To be able to assign a boundary to a k-microcube D k → M, the treatments of [7, 15] I.14, [4, 18 ]I V.1, [16] 4.2.1 all take resort to what [16] calls marked microcubes (and we shall follow this terminology here); these are pairs (τ, d) ,w hereτ : D n → M is a microcube and d = (d1 ,..., dk) ∈ D k .T hen2k boundary faces ∂ α i (τ, d) can naturally be defined as marked k − 1-microcubes...

    Anders Kock. Cubical Version of Combinatorial Differential Forms

    • ...instead of smooth manifolds M one works with the function ring C1(M), etc.) [24], as well as pre-quasi-C -algebras...

    C. J. M. Heunenet al. The Principle of General Tovariance

    • ...For textbooks on synthetic differential geometry, the reader is referred to [5, 7, 9]...

    Hirokazu Nishimuraet al. General Jacobi Identity Revisited Again

    • ...To see how to build such a good topos, the reader is referred to Kock [1] or Moerdijk and Reyes [7]...

    Hirokazu Nishimura. Curvature in Synthetic Differential Geometry of Groupoids

    • ...However, as with every rigorous theory, the consistency of the smooth infinitesimal analysis is provided by the construction of several models of it, as shown in [14] and [15]...
    • ...For further details see Bell [14], Lavendhomme [20], and Moerdijk and Reyes [15]...
    • ...S, by substituting it with a more powerful axiom, in order to get the idea that a smooth function locally behaves exactly as a polynomial of degree n ≥ 1. Of course, this new axiom is still compatible with the construction of a model S (see [15])...

    Riccardo Dossenaet al. Mathematics through Diagrams: Microscopes in Non-Standard and Smooth A...

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