PIE base ‘down’.

In The American Heritage Dictionary of Indo-European Roots, Calvert Watkins gives this PIE root for Greek kata ‘down, downwards; opposite, against’, likening it to the way animals drop their offspring, as Latin catulus ‘young animal; young dog, puppy’ indicates. In which case, other derivatives include catastrophe and catalogue.

However, the Online Etymological Dictionary gives the PIE root for Greek kata as *kmt- ‘down, with, along’. Pokorny does not give this possible root a main heading. However, it does say that the PIE root *kom- is cognate with *kmta ‘besides, along, downwards, with’, which is the root of Greek kata.

I’ll leave Watkins’ link in the Glossary until advised otherwise.

[Pokorny kat-2 ‘to bear young; animal cub’, p. 534.]