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.

The internal logic of a locally cartesian category is expected to be a dependent type theory with dependent sum types, identity types, and a set truncation axiom.

Last revised on March 8, 2024 at 05:31:20. See the history of this page for a list of all contributions to it.