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.