标题： 微分空间的切空间及其变体 显示英文标题

标题： Tangent spaces of diffeological spaces and their variants

摘要： 几种方法已被提出用于定义微分流形的切空间。 其中，内部切函子是作为流形的切函子的左Kan扩张得到的。 然而，该函子的右Kan扩张尚未被充分研究。 在本文中，我们研究了这个右Kan扩张与外部切空间之间的关系，后者是微分流形的另一种切空间类型。 我们证明，通过稍微修改用于右Kan扩张的包含函子，我们得到一个右切空间函子，它几乎与外部切空间同构。 此外，我们表明，当一个微分流形满足一个称为光滑正则的有利性质时，这个右切空间与前面提到的右Kan扩张一致。 显示英文摘要

摘要： Several methods have been proposed to define tangent spaces for diffeological spaces. Among them, the internal tangent functor is obtained as the left Kan extension of the tangent functor for manifolds. However, the right Kan extension of the same functor has not been well-studied. In this paper, we investigate the relationship between this right Kan extension and the external tangent space, another type of tangent space for diffeological spaces. We prove that by slightly modifying the inclusion functor used in the right Kan extension, we obtain a right tangent space functor, which is almost isomorphic to the external tangent space. Furthermore, we show that when a diffeological space satisfies a favorable property called smoothly regular, this right tangent space coincides with the right Kan extension mentioned earlier.