3-Dimensional Quantum Gravity 5. In Zermelo-Fraenkel set theory, everything is a set, the only fundamental relationships between sets are membership and equality, and two sets are equal if and only if they have the same elements. Of course one must bend over backwards to think of such varied entities as sets, so this formalization may seem almost deliberately perverse. However, it represents the culmination of a worldview in which things are regarded as more fundamental than processes or relationships. More recently, mathematicians have developed a somewhat more flexible language, the language of category theory.
Category theory is an attempt to put processes and relationships on an equal status with things.
We write a morphism from to as . We also demand that composition be associative. Perhaps the most familiar example of a category is . Here the objects are sets and the morphisms are functions between sets. However, there are many other examples.