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text: '[summary: Category theory is famously very difficult to understand, even for people with a relatively high level of mathematical maturity. Universal properties are perhaps the easiest important theme of category theory.\n\nWith this project, we want to produce an explanation that will clearly communicate this core concept in category theory, the universal property, to a wide audience of learners.]\n\nCategory theory is famously very difficult to understand, even for people with a relatively high level of mathematical maturity. Universal properties are perhaps the easiest important theme of category theory.\n\nWith this project, we want to produce an explanation that will clearly communicate this core concept in category theory, the universal property, to a wide audience of learners.\n\nThis page is an outline for the project, the below links are to pages within its scope.\n\n1. The idea of [64t not caring about things except up to isomorphism].\n- [4f4]\n2. The idea that [5zt we can describe objects based entirely on how they interact with other objects].\n3. Introduce the [614 category of finite sets], describing the empty set, disjoint union and product\n- [3jz]\n- [5zy]\n- [5zc]\n- [5s8]\n- [5z9]\n- [5zs]\n4. Show how [5zr the empty set can be described entirely by its universal property].\n- [600]\n5. Show how [63m the union] and [5zv product can be described entirely by their universal properties], up to isomorphism.\n6. Introduce a specific [3rb poset] category: [ $\\mathbb{N}$ with an arrow between $a$ and $b$ iff $a$ divides $b$]. (Not sure about this one - maybe it already requires knowing what a category is?)\n7. Describe the least upper bound and greatest lower bounds in a poset; in particular, in $\\mathbb{N}$ under the divisibility relation, we obtain the GCD and the LCM.\n- A page (or two) about [-poset_least_upper_bound] and [-65z] (these actually already exist! [-3rc])\n8. Describe [poset_bound_universal_property the universal properties of the LUB and GLB]; compare them with the union and coproduct.\n9. Wrap up by [universal_property_in_the_wild explaining that this kind of property crops up all over the place].',
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