nLab locally cartesian category

Locally cartesian categories

Locally cartesian categories


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

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

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