超越流形的统治哲学
Beyond the Regnant Philosophy of Manifolds
摘要：
Frolicher空间和光滑映射构成一个Carnival闭范畴。在我们以前的论文[Far East Journal of Mathematical Sciences，35（2009），211-233]中证明了Weil可指数Frolicher空间的满子范畴是Carnival闭的.通过将微线性从一个很好适应的综合微分几何模型中解放到Frolicher空间中，我们得到了Frolicher空间的微线性概念。本文证明了它的Weil可指数微线性Frolicher空间的满子范畴是Carnival闭的. Weil可指数Frolicher空间到Cahiers topos的规范嵌入被证明保持微线性。
英文摘要：
Frolicher spaces and smooth mappings form a cartesian closed category. It was shown in our previous paper [Far East Journal of Mathematical Sciences, 35 (2009), 211-233] that its full subcategory of Weil exponentiable Frolicher spaces is cartesian closed. By emancipating microlinearity from within a well-adapted model of synthetic differential geometry to Frolicher spaces, we get the notion of microlinearity for Frolicher spaces. It is shown in this paper that its full subcategory of Weil exponentiable and microlinear Frolicher spaces is cartesian closed. The canonical embedding of Weil exponentiable Frolicher spaces into the Cahiers topos is shown to preserve microlinearity.
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