Crossword Genius

You may have a nap on it (6)

Ross

I believe the answer is:

carpet

I'm a little stuck... Click here to teach me more about this clue!

'you may' is the definition.
Although both the answer and definition are singular nouns, I don't understand how they can define each other.

'a nap on it' is the wordplay.
I cannot really see how this works, but
'a' is found in the answer.
'it' could be 't' (abbreviation. e.g. in 'tis) and 't' is present in the answer.
This explanation may well be incorrect...

'have' is the link.

Can you help me to learn more?

(Other definitions for carpet that I've seen before include "blanket" , "A red ...... is rolled out for VIPs" , "Dress down" , "Floor-covering" , "On the ......- getting a ticking-off" .)

I've seen this clue in The Globe and Mail.
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