Gravity Walk on Walls and Roof 2D

Hey everyone, got a question for you, how could I get a character to be running, then get to a wall and keep running up that wall and then again for the roof etc. ?

I'm thinking of something with colliders and ray casting but I don't know how I'd code it.. I was also thinking of having it so the walls have a tag and the roof has a tag and then if the player got close enough to that tag, it would run up the wall.

Essentially I want my player to be able to do a full run around the inside of a cube and be able to jump off at any point and land back on the floor when a key is pressed.

I'll be coding in C#

Thanks in advanced!