Depends what route you wanna go down, many involve a world of hurt
Most professional games will have a server that loads the entire map (never renders it obviously), and calculated collisions exactly as you probably are in your single player version. The people 'playing on the server' will also calculate collisions themselves, then just send what they have done (e.g. im moving forward and ended up here or something). This is when the server checks its collisions results with the clients, and send the client a correct version if it went wrong. This is essentially how you stop someone editing their client to cheat and go through walls or always claim they've shot someone, or w/e.
If you're making a small game, or even better if its co-op (no pvp) then this is unnecesary, I don't recommend it anyway as its extremely difficult when compensating for the lag time it takes to send and receive messages.
So really it all depends what your game does.. It may be best just to use the server to tell all the players what each one has done, and forget doing server side collision for now. Once you have that running smooth you can look at what problems exist, and start working on a solution.
But tl'dr your question about how to do it on server side, you keep track of the players state, receive his actions, and check his movement or w/e exactly the same as in singleplayer, so yes you need to load the collision data, be it a tiled array or bunch of squares or w/e
Edit: I just read your other thread about its being a 2d fighting game. That isnt easy, you'll need to do a fair bit of reading up on the subject. GL