# universal property

Definition from Wiktionary, the free dictionary

## English[edit]

### Noun[edit]

**universal property** (*plural* **universal properties**)

- (mathematics) A definition of a mathematical object, up to isomorphism, in terms of abstract maps between it and other objects of the same category. More specifically, it is either the
*initial property*of an initial object in a coslice-like comma category or the*terminal property*of a terminal object in a slice-like comma category; these are roughly analogous to the minimum and the maximum (respectively) of a certain lattice, and are used to define the object uniquely up to isomorphism.