DM K2 Categories Dropdown allows you to list categories inside a dropdown, in a Joomla module; you can choose to list categories having a particular parent;
in addition, the module can show an intro text, a link in the
bottom part, the articles' creation date. You can choose to have the
active item always selected; SEF is supported with native Joomla API. DM K2 Categories Dropdown was designed  K2.joomlaextensions.dmdigital.it/pro-extensions/k2-extensions/dm-k2-categories-dropdown.html