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I want to implement a notion of a category, monoidal category and braided monoidal category in haskell. And I'm not sure if [a] or Data.Set a is a correct notion for representing an objects in a category.

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    How to implement the notion o$f$ a category in Haskell depends on whether you want categories to be values, types, or something else entirely. If a category is a value, as you seem to be wanting, there's no good answer to your question, but I think it may make more sense to make the category be an entire type, rather than just a list or set. That said, I think this is really more of a Haskell question than a math question; I'd suggest posting it on stackoverflow.com for better answers.2011-08-25

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Most categories do not have a set of objects. When this does happen, you have what is called a small category. Despite this, many categories have what is known as a small skeleton, meaning that the category of objects up to isomorphism is small. Such a category is said to be essentially small, and examples of such categories include finite dimensional $k$-vector spaces (for some field $k$) and finite sets.

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    “essentially small” or *svelte*2011-09-02