# 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. --- # Agent Instructions: Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter: ``` GET https://mandober.gitbook.io/math-debrief/450-category-theory/10-categories/set.md?ask= ``` The question should be specific, self-contained, and written in natural language. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.