Petsafe Cat Flaps.
They are designed for installation in solid core wood doors and are a very good value for that application.
Framing would be required for installation in hollow-core or metal doors and would not be recommended. Inside installation only.
The smaller flap is weather-stripped and has a magnetic closure to resist wind.
It also has a built-in sliding lock. The larger 4-way locking version does not include the fuzzy weather stripping.
Petsafe products may not be shipped outside the USA.