The invention relates to a method for cleaning crude terephthalic acid by means of catalytic, hydrogenating aftertreatment using a catalyst material containing at least one hydrogenation metal applied to a carbon carrier consisting of carbon fibres. The invention also relates to a catalyst consisting of the at least one catalyst material containing the at least one hydrogenation metal applied to the carbon fibres, the BET surface of the carbon carrier being 500 m²/g, and a monolithic catalyst consisting of said at least one catalyst material containing the at least one hydrogenation material applied to the carbon fibres, and at least one support element or skeleton element which differs from the catalyst material and is connected to the same, said element mechanically supporting the catalyst material and maintaining the same in a monolithic form. The invention further relates to a method for producing the monolithic catalyst and the use thereof, a reactor containing a plane catalyst material in the form of woven fabric, knitted fabric and/or felt, the use of the same and a method for the selective hydrogenation of carbon-carbon double or triple bonds and/or hydrogenable functional groups in organic compounds containing the same.