Robert's focus is on the possibility of creating a double-categorical programming language which could encode more structure.
“Categories, including double categories, (and, by extent, abstract mathematics) are really cool!”
@thinkingwithcats
Last time, I explained how, given any sort of mathematical structure that can be defined using operations (with finitely many inputs) and rules about what terms are equal, we can define a Lawvere theory that encodes that data in the form of a category. But not all mathematical structures can be defined in this way, […]
In 1963, the PhD thesis of Francis William Lawvere (1937-2023) revolutionized how mathematicians look at algebraic structures, and kickstarted a new branch of mathematics. The main contribution of this thesis: Lawvere theories. Not exactly a self-explanatory name for a concept, so let me explain. Prior to Lawvere’s thesis, the theories of algebraic structures (essentially, the […]
Imagine that you come across a new game, and want to learn how to play it. How would you go about it? Chances are that it would involve reading the rules, watching the game being played, or some combination of the two. These two approaches look vastly different in practice, but they both serve the […]
If you’ve never heard of Mad Libs before, it is a game that presents the player with a skeleton of a short story, with blank spaces interspersed throughout that are each labelled with certain types of words (noun, verb, adjective, etc.). The player fills in the blanks with words of their choice, and is generally […]
For as long as I can remember, I’ve been what I would call a visual learner when it comes to language. I enjoyed my few opportunities to participate in spelling bees when I was in grade school, though my one chance to go to the board-wide contest was dashed by “paramecium” (though on the bright […]
At long last, here we are. We’ve explored categories, internal categories, and functors, all to be able to look at the flavour of category that I have been focused on for the last couple of years: double categories. So, here we go… “A double category is a category with two kinds of morphisms” …is something […]
Okay, so I got a bit ahead of myself at the end of my last post. Remember that we ended off there with this diagram of objects and arrows that somehow encodes the structure of a category, and we asked the question “What if we took this diagram inside some category whose objects themselves were […]
In my previous post, I gave a bit of an overview of my personal favourite brand of abstract structure: categories (if you haven’t read that post yet, then please consider yourself formally, aggressively notified to do so). To briefly summarize the main point of that post (which you should definitely still go read if you […]
Now that I’ve hopefully got you interested in exploring abstraction a bit further (if you already haven’t read my first blog post about abstraction and word games, check it out here), allow me to introduce you to the particular brand of abstraction that I and dozens of mathematicians around the world are dedicating years of […]
What do the following three things have in common: a loaf of bread, a pie, and a golf ball? I encountered this question when I was about 12 years old, on the bus coming home from school. For a few weeks, the radio station that our bus driver liked to have on ran a contest […]
