regular, geometric, and coherent categories

I wrote:

Here's some stuff I think I know. I know the definitions of the above concepts, as long as I have the book open to the right page... but I left it at home, so these could be wrong!

Some were.

Cartesian categories have finite limits. Regular categories are cartesian categories with regular epi/mono factorizations, which must be stable under pullbacks.

Fine.

Geometric categories are regular categories admitting arbitrary unions of subobjects, which must be stable under pullbacks. Coherent categories are geometric categories where pullback of subobjects has a right adjoint (which plays the role of "for all").

These were mixed up.