Do cats adapt

Often it depends on the cat and its personality. Some cats will adapt almost instantly, some may take time, or even find it practically impossible.

If you mean if they adapt to their new surroundings if you move house, then the above applies.

If you mean as a species to different climates, that's another question. That also depends on the cat, and the way it 'is'. For example, if it is very long haired, it won't adapt very well to the Sahara desert. If its not a good hunter, it may take time for it to adapt to having to catch all its own food if its abandoned.