Abyss

A group of people have been mysteriously transported into a structure filled with deadly monsters. When they awake in this dangerous place, they remember little beyond their names, but they each also have a 'trigger.' Their trigger grants them an individual ability that will help them navigate through the dangerous area.

Dan Hibiki wakes up and soon meets the telepath Hiiragi Sakura, radar-girl Misaki Haru, strong-man Kubo Taketo, and psychokinetic Fuse Yuuto. Dan's own ability seems to be to copy that of anyone he is near. They will have to work together strategically if they want any chance of getting out alive!

(Source: MangaHelpers)