You can do this easily with jQuery:
/* Checks if cat is selected when publish button is clicked */
jQuery( '#submitdiv' ).on( 'click', '#publish', function( e ) {
var $checked = jQuery( '#category-all li input:checked' );
//Checks if cat is selected
if( $checked.length <= 0 ) {
alert( "Please Select atleast one category" );
return false;
} else {
return true;
}
} );
The above code will show an alert box if no category is selected. You can use dialog box instead if you’d like.