王进一 (Wang Jinyi), SimplicialCat , 单纯猫 SimplicialCat

Maths 数学

My supervisor is Prof. Lin Chen. 我的导师是陈麟老师.

My mathematical interests lie in 我的数学兴趣 (按时间顺序排列):

• initially, differential geometry, algebraic topology;微分几何, 代数拓扑;
• later, category theory, topos theory, categorical logic,范畴论, 意象, 范畴逻辑;
• homotopy theory, homotopy type theory;同伦论, 同伦类型论;
• and recently, the geometric Langlands program.几何 Langlands 纲领.

Some of my talks are on Bilibili. B 站上有一些我的讲座.

Some of my notes are on Zhihu. 知乎上有一些我的笔记.

Here are my Github repositories. 这里是我的 Github 仓库.

Markdown commutative diagram tool Markdown 交换图生成器

An interactive commutative diagram editor for Markdown. 一个用于 Markdown 的交互式交换图编辑器.

Page 页面

Selected works 数学作品选

These are in Chinese unless specified otherwise. 除特别说明外, 以下资料为中文.

盲人摸象 (Blind men touching an elephant)

A basic introduction to topos theory. 意象理论入门资料.

Book PDF on Github (>300 pages) Github 上有书籍 PDF (>300 页)

单纯百科 Simplopedia

A forest-style site personal encyclopedia of mathematics. 一个forest风格的个人数学百科.

Site 网站

Nonabelian Cohomology English

A short note on nonabelian cohomology, using the language of ∞-toposes. 关于非 Abel 上同调的简短笔记, 使用 ∞-意象的语言.

Notes 笔记

Sketches of an Elephant English

A short talk on topos theory (title borrowed from P. Johnstone) 关于意象理论的简短报告 (标题致敬 P. Johnstone)

Notes 笔记

Interview with Prof. Laurent Lafforgue English

Video 1: From Langlands program to topos theory 视频 1: 从 Langlands 纲领到意象理论

Video 2: The future of topos theory 视频 2: 意象理论的未来

Category Theory in Differential Geometry 微分几何中的范畴学

A short talk on the use of sheaves and stacks in differential geometry. 关于层和叠在微分几何中的用处的简短报告.

Notes 笔记

Quillen's 1969 paper explained English

A presentation of Quillen's 1969 paper on formal group laws. Quillen 1969年关于形式群律论文的介绍.

Notes 笔记

Survey on Atiyah–Singer index theorem English

Article 文章

Spin geometry and Dirac operators 自旋几何与 Dirac 算子

Notes 讲义

Notes on Categorical Logic Summer School 2025 2025 范畴逻辑暑校笔记

Notes 1: Posets and propositional logic 笔记 1: 偏序集与命题逻辑

Notes 2: Lex categories, algebraic theories and locally finitely presentable categories 笔记 2: 左正合范畴, 代数理论, 局部有限可表现范畴

Notes 3: Sketches 笔记 3: 提纲 (Sketches)

Principal bundles in an ∞-topos ∞-意象中的主丛

Video 视频

Slides 讲稿 (幻灯片) English

All concepts are Kan extensions 一切概念都是 Kan 扩张

Video 视频

Non-maths 非数学

Chord Progression Player 和弦进行播放器

A web-based chord progression player. 基于 Web 的和弦进行播放器.

Page 页面

Game of Life 生命游戏

A toy simulator of Conway's Game of Life. Conway 生命游戏的简易模拟器.

Page 页面

Selected musical works 音乐作品选

Que le Vent Soit Doux

An improvised piano re-arrangement of a beautiful background music in Genshin Impact. 原神中一段优美的背景音乐的即兴钢琴改编.

Video 视频