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Introduction: Cheuk Man Hwang

edited May 8 in Chat

I am currently a high school math teacher. I studied contact and symplectic geometry, namely using Seiberg-Witten equations to investigate the Reeb field, in graduate school but unfortunately could not finish my dissertation. Study mathematics becomes a hobby now, I will try to learn as much mathematics as I can during spare time. My first encounter with category theory was when I took courses such as algebraic topology and algebraic geometry. I was amazed by its beauty and power of tying different mathematics together. However, I have only used category theory as a tool but never studied it as a subject. For this reason, I would understand some basic concepts such as functors, natural transformations, limits, and colimits, etc, but never really developed a good intuition of the deeper meaning behind these concepts. I tried to read some books but the formality of the subject make it quite obscure even with my background in pure math. Moreover, it was quite difficult for me to find someone to discuss category theory because people around me would dub the subject as "abstract nonsense". I am happy to find this course with so many people from different backgrounds who are interested in category theory. I just finished reading chapter 1 and the related lectures. I find both the book and Prof. Baez's lectures quite enlightening. I will start working on the problems and contribute to the discussions as much as possible.

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  • 1.

    Hello! We are proceeding very slowly and gently in this course, using a clever trick of Fong and Spivak: instead of discussing categories we are (so far) only discussing preorders. A preorder is a category where there's at most one morphism from any object \(x\) to any object \(y\). This means that all diagrams in this category commute, making the whole subject much easier. Functors get called "monotone functions", colimits get called "joins" and limits get called "meets". We are now working on monoidal preorders, which are a special case of monoidal categories. We are seeing lots of examples of all these ideas.

    I look forward to seeing you in the discussions. Questions, comments, answers... all are welcome!

    Comment Source:Hello! We are proceeding very slowly and gently in this course, using a clever trick of Fong and Spivak: instead of discussing _categories_ we are (so far) only discussing _preorders_. A preorder is a category where there's at most one morphism from any object \\(x\\) to any object \\(y\\). This means that all diagrams in this category commute, making the whole subject much easier. Functors get called "monotone functions", colimits get called "joins" and limits get called "meets". We are now working on monoidal preorders, which are a special case of monoidal categories. We are seeing lots of examples of all these ideas. I look forward to seeing you in the discussions. Questions, comments, answers... all are welcome!
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