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blog.sigfpe.com | ||
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www.jeremykun.com
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| | | | | Previously in this series we've seen the definition of a category and a bunch of examples, basic properties of morphisms, and a first look at how to represent categories as types in ML. In this post we'll expand these ideas and introduce the notion of a universal property. We'll see examples from mathematics and write some programs which simultaneously prove certain objects have universal properties and construct the morphisms involved. | |
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kndrck.co
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| | | | | Prelude State monads, introduced to me during the data61 functional programming course was one of my most memorable encounter with a monad. This was mainly because things only started to clicked and made a tiny bit of sense after a couple of weeks of frustration. This article is my attempt to explain the underlying mechanics of the State Monad to try and relief the frustration of whomever who was in my position. | |
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bartoszmilewski.com
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| | | | | Previously: Sheaves and Topology. In our quest to rewrite topology using the language of category theory we introduced the category of open sets with set inclusions as morphisms. But when we needed to describe open covers, we sort of cheated: we chose to talk about set unions. Granted, set unions can be defined as coproducts... | |
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bartoszmilewski.com
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| | | Previously: Topology as a Dietary Choice. Category theory lets us change the focus from individual objects to relationships between them. Since topology is defined using open sets, we'd start by concentrating on relations between sets. One such obvious relation is inclusion. It imposes a categorical structure on the subsets of a given set $latex X$.... | ||
