Caps Lock as Ctrl with X Window System

First way

 setxkbmap -option "ctrl:nocaps"

Second way

 xmodmap -e "remove Lock = Caps_Lock"
 xmodmap -e "keysym Caps_Lock = Control_L"
 xmodmap -e "add Control = Control_L"

Where to place the code

The code is to be placed in ~/.xsession. If a login manager is used, it should call XSession. For example,

$ cat /usr/share/xsessions/xmonad.desktop
[Desktop Entry]
Name=XMonad
Comment=Lightweight tiling window manager
Exec=/etc/X11/Xsession
Icon=
Type=XSession