# Universal Properties

DevFeed: [Universal Properties](<https://devfeed.tech/articles/universal-properties-40319.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2013/05/24/universal-properties/>)

Published: 2013-05-24T14:53:25Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Category Theory](<https://devfeed.tech/topics/category-theory.md>), [Mathematics](<https://devfeed.tech/topics/mathematics.md>), [function](<https://devfeed.tech/topics/function.md>), [object](<https://devfeed.tech/topics/object.md>)

Tags: [categories](<https://devfeed.tech/tags/categories.md>), [category-theory](<https://devfeed.tech/tags/category-theory.md>), [coproducts](<https://devfeed.tech/tags/coproducts.md>), [examples](<https://devfeed.tech/tags/examples.md>), [function](<https://devfeed.tech/tags/function.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [ml](<https://devfeed.tech/tags/ml.md>), [morphisms](<https://devfeed.tech/tags/morphisms.md>), [object](<https://devfeed.tech/tags/object.md>), [product](<https://devfeed.tech/tags/product.md>), [programming](<https://devfeed.tech/tags/programming.md>), [quotients](<https://devfeed.tech/tags/quotients.md>), [types](<https://devfeed.tech/tags/types.md>), [universal-properties](<https://devfeed.tech/tags/universal-properties.md>)

## AI overview

This tutorial introduces universal properties in category theory, defining initial, final, and zero objects through unique morphisms. It illustrates the concepts with examples from mathematics and Set, and discusses constructing programs related to these properties.

## Source excerpt

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.