Cartesian difference categories are a recent generalisation of Cartesian differential categories which introduce a notion of "infinitesimal" arrows satisfying an analogue of the Kock-Lawvere axiom, with the axioms of a Cartesian differential category being satisfied only "up to an infinitesimal perturbation". In this work, we construct a simply-typed calculus in the spirit of the differential lambda-calculus equipped with syntactic infinitesimals and show how its models correspond to difference lambda-categories, a family of Cartesian difference categories equipped with suitably well-behaved exponentials.
翻译：笛卡尔人差异类别是最近对笛卡尔人差异类别的一种概括,它引入了一种“无限”箭头的概念,它满足了Kock-Lawvere 轴轴的类比,而笛卡尔人差异类别的轴轴仅仅满足了“直至一个极小的轻微扰动 ” 。 在这项工作中,我们根据配有合成无限动物的羊羔差异微积分的精神,构建了一种简单的微积分类型,并展示其模型如何与羊羔-分类(一个配有适当行为良好的指数的喀尔提人差异类别)的区别相吻合。
相关内容
微信扫码咨询专知VIP会员