I'm looking for a reference on internal categories and externalization of internally defined notions.

The nlab has a stub on externalization (more details are available under small fibration) and the page on internal categories gives enough of an introduction that I can sketch most internal notions, but I could really use a concise introduction to internal categories and externalization, and if possible the relationship between internalization and externalization. Are they adjoint in some sense?

I'm fine assuming a background of $2$-category theory, so talking about the $2$-category of internal categories in a category with pullbacks etc. would make sense, but ideally the reference would assume no familiarity with internal category theory or externalization. Any assistance is appreciated.

Sketches of an elephant. $\endgroup$ – Zhen Lin Sep 19 '20 at 0:384more comments