categories
/ˈkætɪɡ(ə)ɹiz/ · cat·e·go·ries
noun
- A group, often named or numbered, to which items are assigned based on similarity or defined criteria. I wouldn't put this book in the same category as the author's first novel.
- A collection of objects, together with a transitively closed collection of composable arrows between them, such that every object has an identity arrow, and such that arrow composition is associative. Just as a monoid consists of an underlying set with a binary operation 'on top of it' which is closed, associative and with an identity, a category consists of an underlying digraph with an arrow composition operation 'on top of it' which is transitively closed, associative, and with an identity at each object.
Did you know? The concept of categories has been widely used in various fields, including science, philosophy, and computer science, to organize and understand complex systems and relationships.