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Finding the fun in good math; Shredding bad math and squashing the crackpots who espouse it.
Mark Chu-Carroll (aka MarkCC) is a PhD Computer Scientist, who works for Google as a Software Engineer. My professional interests center on programming languages and tools, and how to improve the languages and tools that are used for building complex software systems.
Category: Abstract Algebra
Since I mentioned the idea of monoids as a formal models of computations, John Armstrong made the natural leap ahead, to the connection between monoids and monads - which are a common feature in programming language semantics, and a...
Posted by Mark C. Chu-Carroll at 10:57 AM • 5 Comments •
Category: Abstract Algebra
By now, we've seen the simple algebraic monoid, which is essentially an abstract construction of a category. We've also seen the more complicated, but interesting monoidal category - which is, sort of, a meta-category - a category built using...
Posted by Mark C. Chu-Carroll at 1:28 PM • 1 Comments •
Category: Abstract Algebra
In the last post on groups and related stuff, I talked about the algebraic construction of monoids. A monoid is, basically, the algebraic construction of a category - it's based on the same ideas, and has the same properties;...
Posted by Mark C. Chu-Carroll at 6:34 PM • 4 Comments •
Category: Group Theory
This post started out as a response to a question in the comments of my last post on groupoids. Answering those questions, and thinking more about the answers while sitting on the train during my commute, I realized that...
Posted by Mark C. Chu-Carroll at 10:03 PM • 1 Comments •
Category: Group Theory
In my introduction to groupoids, I mentioned that if you have a groupoid, you can find groups within it. Given a groupoid in categorical form, if you take any object in the groupoid, and collect up the paths through...
Posted by Mark C. Chu-Carroll at 12:17 PM • 23 Comments •
Category: Group Theory
Today's entry is short, but sweet. I wanted to write something longer, but I'm very busy at work, so this is what you get. I think it's worth posting despite its brevity. When we look at groups, one of...
Posted by Mark C. Chu-Carroll at 4:12 PM • 16 Comments •
Category: Group Theory
So far, I've spent some time talking about groups and what they mean. I've also given a brief look at the structures that can be built by adding properties and operations to groups - specifically rings and fields. Now,...
Posted by Mark C. Chu-Carroll at 7:18 PM • 16 Comments •
Category: Haskell
As promised, I'm finally going to get to the theory behind monads. As a quick review, the basic idea of the monad in Haskell is a hidden transition function - a monad is, basically, a state transition function. The...
Posted by Mark C. Chu-Carroll at 2:02 PM • 8 Comments •
Category: topology
Suppose we've got a topological space. So far, in our discussion of topology, we've tended to focus either very narrowly on local properties of T (as in manifolds, where locally, the space appears euclidean), or on global properties of T....
Posted by Mark C. Chu-Carroll at 5:19 PM • 13 Comments •
Category: topology
This is going to be a short but sweet post on topology. Remember way back when I started writing about category theory? I said that the reason for doing that was because it's such a useful tool for talking about...
Posted by Mark C. Chu-Carroll at 4:43 PM • 2 Comments •
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