论文标题
光滑歧管类别中的向量束和差束
Vector bundles and differential bundles in the category of smooth manifolds
论文作者
论文摘要
切线类别是配备有内压器的类别，可满足某些公理，该公理可以从经典的微分几何形状中捕获切线束函数的抽象属性。 Cockett和Cruttwell在2017年引入了差异束，作为任意切线类别中向量束的代数替代品。在本文中，我们证明平滑歧管类别中的差异捆绑包精确地是向量束。特别是，这意味着我们可以给出向量束的表征，该载体束显示它们是切线分类基本上是代数理论的模型。
A tangent category is a category equipped with an endofunctor that satisfies certain axioms which capture the abstract properties of the tangent bundle functor from classical differential geometry. Cockett and Cruttwell introduced differential bundles in 2017 as an algebraic alternative to vector bundles in an arbitrary tangent category. In this paper, we prove that differential bundles in the category of smooth manifolds are precisely vector bundles. In particular, this means that we can give a characterisation of vector bundles that exhibits them as models of a tangent categorical essentially algebraic theory.
