Nothing about a roll of tape looks like hero equipment, which is exactly why U.A. hands it out during training. In team exercises it settles the argument cleanly: get it wrapped around an opponent and that opponent is finished, no debate about who won the exchange.
Capture Tapes are training tools that U.A. High School issues for certain classroom exercises. They appear early in the series, showing up in chapter 9 of the manga and episode 7 of the anime.
They come as plain rolls of tape, deployed in team battle drills built around taking opposing members out of play. Getting the tape wound around a beaten opponent counts as evidence that the capture happened, and the student on the receiving end is out of the match from that moment.

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Capture Tape is a training tool that U.A. High School issues to its students for certain classroom exercises, taking the form of a plain roll of tape used to signal when an opponent has been taken out of a drill.
U.A. deploys Capture Tape in team battle drills built around taking opposing students out of play, where it functions as the tool that ends a student's part in the exercise.
A student wins a Capture Tape exchange by winding the tape around a beaten opponent. That counts as evidence the capture happened, and the opponent is out of the match from that moment.
U.A. High School itself issues Capture Tape to its students for their practical training exercises.
Capture Tape first appears early in the series, in chapter 9 of the manga and episode 7 of the anime.
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