How do I check on eggs?

New player here, as far as I understand you get eggs from the gacha (which I did) and then need to clear floors to hatch them. I finished my first run, went back to main menu, and did a gacha pull to get what I think was 1 epic and 4 common. Where can I see the eggs and their progress towards hatching? There's no option to check on the starter select screen.