nLab locally cartesian category

Definitions

A category $C$ is locally cartesian if each of its slice categories $C/x$ is a cartesian monoidal category, meaning that $C/x$ has all finite products. Another way to say this is that $C$ has all finite fibred products or equivalently that $C$ has all pullbacks.

A finitely complete category is precisely a locally cartesian category that has a terminal object.

Related entries

• locally cartesian closed category