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qchu.wordpress.com | ||
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bartoszmilewski.com
Abstract: I derive a free monoidal (applicative) functor as an initial algebra of a higher-order functor using Day convolution. I thought I was done with monoids for a while, after writing my Monoids on Steroids post, but I keep bumping into them. This time I read a paper by Capriotti and Kaposi about Free Applicative... |
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www.jeremykun.com
Last time we defined and gave some examples of rings. Recapping, a ring is a special kind of group with an additional multiplication operation that "plays nicely" with addition. The important thing to remember is that a ring is intended to remind us arithmetic with integers (though not too much: multiplication in a ring need not be commutative). We proved some basic properties, like zero being unique and negation being well-behaved. |
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mattbaker.blog
Test your intuition: is the following true or false? Assertion 1: If $latex A$ is a square matrix over a commutative ring $latex R$, the rows of $latex A$ are linearly independent over $latex R$ if and only if the columns of $latex A$ are linearly independent over $latex R$. (All rings in this post... |
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bartoszmilewski.com
This is part 31 of Categories for Programmers. Previously: Lawvere Theories. See the Table of Contents. There is no good place to end a book on category theory. There's always more to learn. Category theory is a vast subject. At the same time, it's obvious that the same themes, concepts, and patterns keep showing up... |
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