Does the nth char equal the nth from last char?

JavaScript (ES6), 26 bytes

s=>n=>s[n]==s.substr(~n,1)

Alternatively:

s=>n=>s[n]==s.slice(~n)[0]

This one almost works, but fails when n == 0 (because s.slice(-1,0) == ""):

s=>n=>s[n]==s.slice(~n,-n)

Another 26-byte solution that @RickHitchcock pointed out:

s=>n=>s[n]==s[s.length+~n]

Jelly, 5 4 bytes

=UƓị

Try it online!

There should be no shorter answers in Jelly. An program would need comparison, reversal/negation, an index call, and a byte for control flow (Ɠ in this case), which adds up to four bytes.

How it works

 =UƓị 
       - (implicit) input string
 =     - equals (vectorizing by characters because a string is a charlist)
  U    - the reversed string
    ị  - get the element at the index of:
   Ɠ   - the input index

-1 byte thanks to @ais523, using Ɠ

MATL, 5 bytes

tP=w)

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Explanation:

t   % Duplicate the input

Stack:
    ['ppqqpq' 'ppqqpq']

P   % Reverse the top element of the stack

Stack:
    ['ppqqpq' 'qpqqpp']

=   % Equals. Push an array of the indices that are equal

Stack:
    [[0 1 1 1 1 0]]

w   % Swap the top two elements

Stack:
    [[0 1 1 1 1 0], 3]

)   % Grab the a'th element of b