# Retina, 62 bytes

    [a-z]
    abcdefghijklmnopqrstuvwxyz
    [A-Z]
    ABCDEFGHIJKLMNOPQRSTUVWXYZ

The two short lines are the regex to match. If the input is lowercase (in the range `[a-z]`), it replaces that character (in this case, that is the entire input) with the lowercase alphabet. The process is similar for uppercase. If it's not a letter, no replacements are made, and it is outputted untouched.

[Try it online.](http://retina.tryitonline.net/#code=W2Etel0KYWJjZGVmZ2hpamtsbW5vcHFyc3R1dnd4eXoKW0EtWl0KQUJDREVGR0hJSktMTU5PUFFSU1RVVldYWVo&input=QQpmCj8)