| Description: |
Category theory studies the algebra of functions under the operation of composition, and develops the viewpoint that most mathematical objects can be defined by the way they connect to other objects in their external environment through functions, rather than by referring to their internal set-membership structure.
A category might be a single object, like a group, vector space or topology; or it might be the whole universe of entities representing an entire branch of mathematics, such as the category of all vector spaces, representing linear algebra. Categories occur everywhere. Their study reveals new mathematical concepts, and provides a powerful language that has become essential for describing many parts of mathematics, as well as playing an important role in the foundations of logic, computer science, theoretical physics, and other subjects. |
