Diolic代数中的微分学函子
Functors of Differential Calculus in Diolic Algebras
摘要：
我们提出了一种新的代数形式来研究向量丛中的微分学。这是通过研究各种函子的微分学在任意分次交换代数（DCGCA）和应用这种语言，特别是简单的一类两个组件的分级对象介绍了这项工作，我们称之为Diolic代数。一个显着的特点，这种概念的方法，微积分是，它恢复了许多著名的对象和概念，从普通微分，辛和泊松几何，但也提供了一些独特的方面，这是自己的独立利益。
英文摘要：
We pose a new algebraic formalism for studying differential calculus in vector bundles. This is achieved by studying various functors of differential calculus over arbitrary graded commutative algebras (DCGCA) and applying this language to a particularly simple class of two-component graded objects introduced in this work, that we call Diolic algebras. A salient feature of this conceptual approach to calculus is that it recovers many well-known objects and notions from ordinary differential, symplectic and Poisson geometry but also provides some unique aspects, which are of their own independent interest.
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