It's a fairly early spoiler, but still a spoiler
The cat goes into the dungeon with him, and is initially treated as a pet. Pretty quickly, though, the cat gets an upgrade that turns her into her own character, and they become something of an iconic duo.
Also, I don't know that I'd necessarily call it sci-fi, maybe more fantasy with... well. it's complicated. In any case, I enjoyed it, and the rest of the series and highly recommend it.