Looping videos from YouTube
∞(And from lots of other places, see youtube-dl --list-extractors for a list.)
# Download a video
$ youtube-dl https://www.youtube.com/watch?v=aZvDe3box70
# Loop the video
$ mpv --no-video --loop=inf --end 3:47 'Shaban - Ungleichung-aZvDe3box70.mkv'
Note the --loop=inf parameter.  And --end <timestamp> is also very helpful.
Also, don’t forget that mpv can play any video that’s downloadable by youtube-dl directly!  (But we can’t use that for looping, because then it would download the file repeatedly.)