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Dimensions in Soda Dungeon are part of the progression of the game.
Once you have defeated the boss of a dimension, the first being on level 100, you will gain access to the portal outside of your tavern. This comes with a number of effects, it acts as a sort of 'soft' restart, removing your current equipment, dungeon levels, gold, and sodas. Other upgrades in the tavern and VIP areas should remain unaffected, and essence will not be reset.
When you travel to the next dimension you will be given a choice of 'Relic' sodas, as well as a pre-determined relic that boosts the stats and abilities of a particular hero type permanently.
By progressing through dimensions the story line is progressed, with a new boss unlocked for each dimension.
There are 10 different bosses. Then you'll reach the final dimension, called warrior dimension (WD). From that point on levels will still increment in dungeon exploration, but cycle through the same bosses.