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Hi all! A few years ago I did Part III at Cambridge where I took several category theory courses and wrote an essay on fibered categories. Despite all of this I never "felt it in my bones" the way I feel about other branches of mathematics. In this course, I'm hoping to gain more intuition about category theory and learn about how it can apply to real world relationships, e.g. the relationship between a branch and a tree or between all things that are the color yellow. While researching for my essay I stumbled upon the definitions of stuff, structure, and properties via category theory. They were beautiful and got to the heart of my intuition about these terms. I wonder how far this analogy can be pushed towards real-world stuff, structure, and properties.
Since Cambridge, I have been teaching middle school computer science but am leaving to start my PhD in math next fall!