Subobject classifier

In the mathematical field of category theory, a subobject classifier is a special object ${\displaystyle \Omega }$ of a category such that, informally, the subobjects of any object ${\displaystyle X}$ correspond to the morphisms from ${\displaystyle X}$ to ${\displaystyle \Omega }$. This provides an analogue of the set of Booleans${\displaystyle \{0,1\}}$ in categories other than the category of sets.

The main use of subobject classifiers is in topos theory, where an elementary topos is defined as a category with a subobject classifier and certain additional requirements. In the internal language of an elementary topos, the subobject classifier is used to interpret truth values, hence the alternative name “object of truth values”.