# Joyal's CatLab set

## Definition

• A [set] is a collection of distinct objects, called the elements of the set. Two sets are equal if they have the same elements. Formally, we write $a\in S$ to indicate that $a$ is an element of the set $S$.

• A [set] can be small or large, but this notion is purely formal and it depends on the choice of a theory of sets.

Created on January 19, 2010 at 02:22:22 by joyal