Assembly comprising a hob supported by a frame and an extractor hood suitable for being mounted in a worktop intended to support the hob; the extractor hood comprises: - a frame comprising a base plate from where external lateral walls rise, and an upper plate from where internal lateral walls rise; the internal lateral walls being provided with extraction openings disposed in upper longitudinal position to let the air pass; - a lower chamber defined between the base plate and the upper plate; - two lateral chambers defined between the external lateral walls and the internal lateral walls; the lateral chambers being in communication with the lower chamber; - filter units disposed in the lateral chambers; - lids that cover the lateral chambers on the filter units; - a fan disposed in a box in communication with the lower chamber; - a housing defined between the upper plate and the internal lateral walls of the frame of the extractor hood; wherein said frame of the hob is mounted with the possibility of sliding vertically in said housing of the frame of the extractor hood in order to move from a raised position, wherein the hob is at the level of the lids of the lateral chambers, to a lowered position, wherein the hob is under the level of the lids of the lateral chambers, in such a way as to free the extraction openings of the lateral walls of the frame of the extractor hood; said assembly comprising: - drive means to drive the vertical translation movement of the frame of the hob relative to the frame of the extractor hood; and - actuation means (5; 105; 205; 305; 405) to move said hob. the extractor hood comprises: - a frame comprising a base plate from where external lateral walls rise, and an upper plate from where internal lateral walls rise; the internal lateral walls being provided with extraction openings disposed in upper longitudinal position to let the air pass; - a lower chamber defined between the base plate and the upper plate; - two lateral chambers defined between the external lateral walls and the internal lateral walls; the lateral chambers being in communication with the lower chamber; - filter units disposed in the lateral chambers; - lids that cover the lateral chambers on the filter units; - a fan disposed in a box in communication with the lower chamber; - a housing defined between the upper plate and the internal lateral walls of the frame of the extractor hood; - a frame comprising a base plate from where external lateral walls rise, and an upper plate from where internal lateral walls rise; the internal lateral walls being provided with extraction openings disposed in upper longitudinal position to let the air pass; - a lower chamber defined between the base plate and the upper plate; - two lateral chambers defined between the external lateral walls and the internal lateral walls; the lateral chambers being in communication with the lower chamber; - filter units disposed in the lateral chambers; - lids that cover the lateral chambers on the filter units; - a fan disposed in a box in communication with the lower chamber; - a housing defined between the upper plate and the internal lateral walls of the frame of the extractor hood; wherein said frame of the hob is mounted with the possibility of sliding vertically in said housing of the frame of the extractor hood in order to move from a raised position, wherein the hob is at the level of the lids of the lateral chambers, to a lowered position, wherein the hob is under the level of the lids of the lateral chambers, in such a way as to free the extraction openings of the lateral walls of the frame of the extractor hood; said assembly comprising: - drive means to drive the vertical translation movement of the frame of the hob relative to the frame of the extractor hood; and - actuation means (5; 105; 205; 305; 405) to move said hob. - drive means to drive the vertical translation movement of the frame of the hob relative to the frame of the extractor hood; and - actuation means (5; 105; 205; 305; 405) to move said hob.