When you watch a 4K video on a 1080p monitor, it will not be in its original 4K quality. Instead, the video will be downscaled to 1080p. This is because a 1080p monitor can only display a maximum resolution of 1920x1080 pixels, while a 4K video has a resolution of 3840x2160 pixels.
When a 4K video is played on a 1080p monitor, the video will be resized to fit the lower resolution of the monitor. This means that the video will be compressed and some of the detail and quality will be lost. The resulting image will still be a high-definition image, but it will not be as sharp and clear as the original 4K video.
In summary, when you watch a 4K video on a 1080p monitor, it will be downscaled to 1080p quality. While it will still be a high-definition image, it will not be as clear and sharp as the original 4K video.