ABSTRACT
Category theory begins with the concept of an arrow. A category is a collection of arrows satisfying certain natural axioms regarding their existence and their composition. A way out of this paradoxical situation is to define a set in such a way that the gathering of all the so-defined sets is not a set, unambiguously. This can be achieved by appealing to properties of the operation of the gathering of elements, like certain natural notions of being able to form a larger gathering by the concatenating of smaller gatherings. An arrow, commonly also called a morphism or a map or a transformation, is assumed to have associated with it a source and a target. Any composition of arrows leads ultimately to some arrow within the same category. A statement or a property related to a category then consists only of arrows and objects within that category.
