The core diagram of a double Lie algebroid consists of the core of the double Lie algebroid, together with the two core-anchor maps to the sides of the double Lie algebroid. If these two core-anchors are surjective, then the double Lie algebroid and its core diagram are called transitive. This paper establishes an equivalence between transitive double Lie algebroids, and transitive core diagrams over a fixed base manifold. In other words, it proves that a transitive double Lie algebroid is completely determined by its core diagram.The comma double Lie algebroid associated to a morphism of Lie algebroids is defined. If the latter morphism is one of the core-anchors of a transitive core diagram, then the comma double algebroid can be quotiented out by the second core-anchor, yielding a transitive double Lie algebroid, which is the one that is equivalent to the transitive core diagram.Brown's and Mackenzie's equivalence of transitive core diagrams (of Lie groupoids) with transitive double Lie groupoids is then used in order to show that a transitive double Lie algebroid with integrable sides and core is automatically integrable to a transitive double Lie groupoid.

中文翻译：

---

通过核心图传递双李代数

双李代数的核图由双李代数的核和双李代数两侧的两个核-锚图组成。如果这两个核锚是满射的，那么双李代数及其核图就称为可传递的. 本文建立了传递双李代数和固定基流形上传递核心图之间的等价关系。换言之，证明了传递双李代数完全由其核心图决定。定义了与李代数态射相关的逗号双李代数。如果后一个态射是传递核图的核锚之一，那么逗号双代数可以被第二核锚商出，产生传递双李代数，它等价于传递核核心图。 Brown's and Mackenzie'