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...
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Posted on March 11, 2008 10:57 AM • 5 Comments •
While doing some reading on rings, I came across some interesting stuff about Monoids and syntax. That's right up my alley, so I decided to write a post about that....
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Posted on March 6, 2008 9:39 PM • 3 Comments •
When I first talked about rings, I said that a ring is an algebraic abstraction that, in a very loose way, describes the basic nature of integers. A ring is a full abelian group with respect to addition -...
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Posted on March 4, 2008 9:58 AM • 20 Comments •
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...
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Posted on February 28, 2008 1:28 PM • 1 Comments •
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;...
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Posted on February 18, 2008 6:34 PM • 4 Comments •
In the last couple of posts, I showed how we can start looking at group theory from a categorical perspective. The categorical approach gives us a different view of symmetry that we get from the traditional algebraic approach: in...
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Posted on February 10, 2008 9:28 PM • 3 Comments •
