"downy or woolly surface of cloth," mid-15c., noppe, from Middle Dutch or Middle Low German noppe "nap, tuft of wool," probably introduced by Flemish cloth-workers. Cognate with Old English hnoppian "to pluck," ahneopan "pluck off," Old Swedish niupa "to pinch," Gothic dis-hniupan "to tear."
"have a short sleep," Middle English nappen, from Old English hnappian (Mercian hneappian) "to doze, slumber, sleep lightly," a word of unknown origin, apparently related to Old High German hnaffezan, German dialectal nafzen, Norwegian napp. In Middle English also "be sleepy, be inattentive or careless." Related: Napped; napping.
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<a href="https://www.etymonline.com/word/napping">Etymology of napping by etymonline</a>
Harper, D. (n.d.). Etymology of napping. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/napping