User blog comment:Deedlit11/My humble extension of FOOT/@comment-5529393-20170117081155/@comment-1605058-20170122104815

The \(f_\gamma\) are not separate parameters. \(FOFT_\alpha^\beta\) has one parameter \(\Pi\) being the product of all \(f_\gamma\), and thanks to that we can, for example, refer to any \(f_\gamma\) by speaking of the \(\gamma\)th component of \(\Pi\). This allows quantification over these \(f_\gamma\) or whatever.