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| | www.joachim-breitner.de
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| | igstan.ro
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| | [AI summary] The author provides an intuition for contravariant functors in Scala by explaining the contramap method through the example of deriving custom orderings from standard ones.
| | blog.ploeh.dk
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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.