Connected Lie Groupoids are Internally Connected and Integral Complete in Synthetic Differential Geometry

Symmetry Integrability and Geometry-Methods and Applications

article

Matthew Burke

关键词: Lie theory;    Lie groupoid;    Lie algebroid;    category theory;    synthetic dif ferential geometry;    intuitionistic logic;   

DOI  :  10.3842/SIGMA.2017.007

来源: National Academy of Science of Ukraine

【 摘 要 】

We extend some fundamental definitions and constructions in the established generalisation of Lie theory involving Lie groupoids by reformulating them in terms of groupoids internal to a well-adapted model of synthetic differential geometry. In particular we define internal counterparts of the definitions of source path and source simply connected groupoid and the integration of $A$-paths. The main results of this paper show that if a classical Hausdorff Lie groupoid satisfies one of the classical connectedness conditions it also satisfies its internal counterpart.

【 授权许可】

Unknown