A cylinder, which is part of a folder, includes a cylinder body with at least one gripper that can be moved between a retracted position within the cylinder body; an extended position, and a clamping position in which a tip of the gripper presses flat material against a surface section of the cylinder body. A pivot axis, about which the gripper pivots between its retracted position and its extended position, is within the cylinder body. A counterthrust element, which cooperates with a separate cutting blade, to cut the flat material which is to be gripped by the gripper, is associated with the cylinder body. The gripper is situated upstream of the counterthrust element, in the rotational direction of the gripper cylinder. A second axis, about which the gripper moves in the peripheral direction of the cylinder, is also provided. Both of these axes are fixed in relation to the cylinder.