> For the complete documentation index, see [llms.txt](https://mandober.gitbook.io/math-debrief/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mandober.gitbook.io/math-debrief/450-category-theory/10-categories/set.md).

# Set category

`𝗦𝗲𝘁` is a category of "small" sets as objects, and set-theoretic functions as morphisms.

The "small" attribute of sets is there to make sure included sets all come from a predefined universe, so as to avoid paradoxes that arise from constructing unchecked sets, like a set of all sets that don't include themselves, i.e. have themselves as a member. Consequently, this concern also arises with the category of all categories, `𝗖𝗮𝘁`, that contains only "small" categories for its objects.

`𝗦𝗲𝘁` category is one of the central categories since the definition of many categorical things include it or are related to it. For instance, a concrete category is defined as a category equipped with a faithful functor to the 𝗦𝗲𝘁 category.