发表机构
Instituto de Matemática Pura e Aplicada; Georg-August-University of Göttingen（巴西国家数学研究所; 哥廷根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文从单纯观点研究双李群胚的态射，扩展余对角函子至主双纤维丛和方形态射，并应用于非阿贝尔gerbes模型等价及传递Courant algebroid中Manin三元组的积分细化，证明积分在辛Morita等价意义下良定义。
AI 中文摘要
受广义Kähler几何近期发展的启发，我们从单纯观点研究双李群胚的态射。我们证明余对角函子$\Wbar$从对象扩展到水平和垂直主双纤维丛以及方形$(1,1)$-态射。后者确定了李2-群胚的anafunctor之间的方形和球形二维态射。我们通过两个应用来说明这些构造：首先，我们重新审视非阿贝尔gerbes的两种模型之间的等价性：群胚丛gerbes和主2-丛。我们证明一个主2-丛及其关联的群胚丛gerbe确定了从流形到相应结构李2-群的等价anafunctor。其次，我们细化传递Courant algebroid中Manin三元组的积分。我们证明，在同一个Courant algebroid中，与不同选择的正交Manin三元组相关联的积分通过辛Morita等价相关联。因此，背景Courant algebroid的所得积分在辛Morita等价意义下是良定义的。
英文摘要
Motivated by recent developments in generalized Kähler geometry, we study morphisms of double Lie groupoids from a simplicial viewpoint. We show that the codiagonal functor $\Wbar$ extends from objects to horizontal and vertical principal bibundles and to square-shaped $(1,1)$-morphisms. The latter determine 2-dimensional morphisms of square and globular shape between anafunctors of Lie 2-groupoids. We illustrate these constructions through two applications: First, we revisit the equivalence between two models of nonabelian gerbes: groupoid bundle gerbes and principal 2-bundles. We show that a principal 2-bundle and its associated groupoid bundle gerbe determine equivalent anafunctors from a manifold to the corresponding structure Lie 2-group. Second, we refine the integration of Manin triples in transitive Courant algebroids. We show that integrations associated with different choices of suitably transverse Manin triples in the same Courant algebroid are related by symplectic Morita equivalences. Consequently, the resulting integration of the background Courant algebroid is well defined up to symplectic Morita equivalence.
Comments54 pages, 19 figures
