nLab bicartesian preordered object

Idea

The notion of a prelattice internal to a finitely complete category.

Definition

In a finitely complete category $C$, a bicartesian preordered object or prelattice object is a preordered object $X$ that is both a cartesian monoidal preordered object and a cocartesian monoidal preordered object.

See also

• prelattice

• cartesian monoidal preordered object

• cocartesian monoidal preordered object

• bicartesian closed preordered object

• lattice object

• bicartesian category