课程题目: Fundamental groups and category theory

授课人（Speaker）：Andrey Lazarev，Lancaster University

授课地点(Location)：  吉林大学数学楼第五研讨室

Abstract: This course introduces some of the basic notions of category theory such as natural constructions (functors) and equivalence of categories. The category of sets with a group action is studied as an example.  This category is then related to the category of covering spaces on a given topological space (this part requires learning or taking on trust some of the results of Minicourse 1). If time permits, an outline of Galois theory as an equivalence of categories will be given.

(1) 14:30-15:30, July 6, 2025, Categories, functors and equivalence of categories

(2) 14:30-15:30, July 7, 2025, The category of sets with a group action. Orbits and stabilizers.

(3) 14:30-15:30, July 9, 2025, Classification of covering spaces as an equivalence of categories.

(4) 14:30-15:30, July 10, 2025, Outline of Galois theory as an equivalence of categories. Analogy with covering spaces.

报告人简介：Andrey Lazarev，英国兰卡斯特大学教授，从事代数拓扑与同伦论的研究，曾担任 Bull. Lond. Math. Soc.杂志主编，在Adv. Math.、 Proc. Lond. Math. Soc.、 J. Noncommut. Geom.等杂志上发表多篇高水平论文。