There are many ways to start a blog, and I have decided to choose the one more travelled by.
What this blog is about
Aside from trying to keep my personal life and this blog separate, there are not many constraints to what I am willing to blog about. Basically anything I see as a positive contribution to the Internet goes. A sizeable portion of this blog will be devoted to mathematics, and proofs will be explicit when given. Apart from mathematics, I will be blogging about various other issues that I think I know enough about to be able to say something of value. These areas might include philosophy (though hopefully not very much of it), politics, religion, literature and the sciences. Basically:
Come for the mathematics, stay for all the other interesting stuff.
Because I want to maintain the quality of the posts herein, I will not blog very often.
Who I am
Without going into any existential questions – I am a mathematics student living in a first-world country who now has a blog. I go by Matty Wacksen, a name that is a fairly obscure reference to a literary character (if you can guess what to, tell me) and has very little to do with my real name. I ask anyone who thinks they know my actual name to refrain from posting it. Mathematics plays a much smaller part in my life than in this blog, which is one of the reasons why I will not be posting very often.
The “Observations” part should not need any more explanation. A Category is a set1 (whose elements we call ‘objects’) and some “arrows”. An arrow goes from one object (its domain) to another object (its codomain), and there can be any number of arrows between any given pair of objects. Arrows are composable (if the codomain of the first arrow is the domain of the second one), with composition being associative. Lastly, every object has an identity arrow that is the right and left identity for composition with any arrows that can be composed with it.
All of this has very little to do with the content of this blog. However,the categorical point of view that focuses less on the objects in a category, and more on the arrows between them will hopefully feature in most mathematical posts.
The main reason for using “Categorical” is actually that this blog is very mathematics-heavy and I wanted to use a title that reflects that.
- Actually “set” is not completely accurate as we run into foundational issues once we look at something like the “category of sets”. Some authors therefore use “collection” instead of “set”. ↩