General structure of a mathematics area
It is typical that an area of mathematics busies itself with a specific category, therefore an MOC for subarea of maths should generally have the following structure.
- Objects — Outlines the object of study and some basic properties of it.
- Morphisms — How these objects relate to each other
- Internally — Things constructed “inside” the object, e.g. subsets and elements of a space.
- Externally — The creation of objects from other objects, usually by category-theoretic constructions.
MOCs following this structure
- Category theory MOC dogfooding itself
- Topology MOC
- Group theory MOC