The stage musical Cats was written (music) by Andrew Lloyd Webber, based on poems by T. S. Eliot in Old Possum’s Book of Practical Cats.

If you meant the lyrics/text:

  • Most of the words are directly T. S. Eliot’s poems.
  • Additional lyrics (including much of “Memory”) were written by Trevor Nunn, with contributions from Richard Stilgoe.

So in everyday terms, people usually say: Cats was “written by Andrew Lloyd Webber,” inspired by T. S. Eliot’s poetry.