A Synthetic Version of Lie's Second Theorem

作者：Burke Matthew^*

来源：Applied Categorical Structures, 2018, 26(4): 767-798.

DOI：10.1007/s10485-018-9518-2

• Lie theory
• Lie groupoid
• Lie algebroid
• Category theory
• Factorisation system
• Synthetic differential geometry
• Intuitionistic logic

We formulate and prove a generalisation of Lie's second theorem that integrates homomorphisms between formal group laws to homomorphisms between Lie groups. Firstly we generalise classical Lie theory by replacing groups with groupoids. Secondly we include groupoids whose underlying spaces are not smooth manifolds. The main intended application is when we replace the category of smooth manifolds with a well-adapted model of synthetic differential geometry. In addition we provide an axiomatic system that provides all the abstract structure that is required to prove Lie's second theorem.

• 出版日期2018-8