From The Collaborative International Dictionary of English v.0.48:
Nap \Nap\ (n[a^]p), v. i. [imp. & p. p. Napped (n[a^]pt); p.
pr. & vb. n. Napping (n[a^]p"p[i^]ng).] [OE. nappen, AS.
hn[ae]ppian to take a nap, to slumber; cf. AS. hnipian to
bend one's self, Icel. hnipna, hn[imac]pa, to droop.]
1. To have a short sleep; to be drowsy; to doze. --Chaucer.
[1913 Webster]
2. To be in a careless, secure state; to be unprepared; as,
to be caught napping. --Wyclif.
[1913 Webster +PJC]
I took thee napping, unprepared. --Hudibras.
[1913 Webster]
From The Collaborative International Dictionary of English v.0.48:
Napping \Nap"ping\, n.
1. The act or process of raising a nap, as on cloth.
[1913 Webster]
2. (Hat Making) A sheet of partially felted fur before it is
united to the hat body. --Knight.
[1913 Webster]
3. The act or process of having a short sleep; as, napping is
a common occupation for cats.
[PJC]