Thin-disk lasers are indispensable in photonics research as well as in a multitude of industrial applications. They represent a unique class of laser and amplifier architecture that provides kW output power with excellent properties concerning beam quality, long-term stability, thermal management, and power scalability. For many applications, a reduced complexity of the laser and its size would be highly beneficial. The necessary multipass transitions in thin-disk lasers and amplifiers typically require sophisticated multi-mirror arrangements. Here, we present a monolithic version of the pump concept for thin-disk lasers and amplifiers, where the thin disk is replaced by a thin, wedged gain medium acting as a wedged optical trap. The wedge is coated in a peculiar manner in order to allow for efficient in-and out-coupling of the pump and laser radiation from the wedge. This concept transfers the complexity of the multi-mirror optics into the thin disk itself in a monolithic fashion. With this concept, we achieved 890 W of CW output power, 59% slope efficiency, optical-to-optical efficiency of 50%, and a gain factor greater than 10 for small signals. This demonstrates that this new concept is capable of reaching the kW power regime with minimum complexity and size. Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.