From Bulbapedia, the community-driven Pokémon encyclopedia.
Gateway Colosseum is the first Colosseum in Pokémon Battle Revolution. The battle theme is Rental battles like in the Battle Factory in Pokémon Emerald. The Colosseum leader is Joe. Like most other Colosseums, there are 7 battles in all.
Gateway Colosseum floats at the entrance to Pokétopia and is lit by bright neon lights. All battles here are depicted as happening at night.
After you beat the game, you are allowed to participate in a Battle Swap after each battle. This involves permanently trading one of your Pokémon for one of the opponents Pokémon. This can only be utilized using the Level 50 All rule. This battle theme is called "Trade Battle".
Beating Gateway Colosseum for the first time in Level 30 mode gets you a Bronze Badge, a custom Battle Pass with Gateway Colosseum in the background, and some Poké Coupons. Beating Gateway for the first time in Level 50 All mode unlocks 37 pieces of gear in the shop.
The Pokemon and Trainers are not set, except during the first time you battle there, at Rank 1 Level 30 All. The Trainers, and the Pokemon they have, go as the following during Rank 1: