Category theory is what you get when you take mappings instead of sets as the primitive objects of your universe. At first this might seem a perverse thing to do as mappings seem more complex than sets, but that is just because traditionally mappings have usually been defined in terms of sets.
In set theory you can specify that two sets be equal and you can also specify that one set be an element of another.
In category theory you can specify that two mappings be equal and you can also specify that two mappings compose end to end to produce a third mapping.
Category theory can be used to express some requirements in a very concise way.
In set theory you can specify that two sets be equal and you can also specify that one set be an element of another.
In category theory you can specify that two mappings be equal and you can also specify that two mappings compose end to end to produce a third mapping.
Category theory can be used to express some requirements in a very concise way.