Due to James Dolan and John Baez, this principle states
Microcosm principle: Certain algebraic structures can be defined in any category equipped with a categorified version of the same structure.
A standard example is a monoid object being defined in a monoidal category. The term arises from the idea that the monoid object (the ‘microcosm’) can only thrive in a category (a ‘macrocosm’) that resembles itself.