Conditional bracketing in macro

Question

I am trying to make a macro for typesetting higher-categories, and would like to automatically enclose the optional argument in brackets if it is an expression containing + or -.

In particular I would like to have something like \cat[<optional_rank>]{<name>}, so that for example \cat{Bord}, \cat[n]{Fus}, and \cat[2]{Rep} typeset Bord, nFus, and 2Rep respectively, but \cat[n+1]{Fus} and \cat[n-k-2]{Rep} typeset (n+1)Fus and (n-k-2)Rep respectively.

How can I achieve the automatic bracketing? I am almost sure that the answer will involve xparse, but I don't know how to do it myself.

For convenience here is a MWE (that does not do exactly what I want yet)

\documentclass{article}

\newcommand{\cat}[2][]{{#1}\mathbf{#2}}

\begin{document}
    \(\cat{Bord}\), \(\cat[n]{Fus}\), \(\cat[2]{Rep}\), \(\cat[n+1]{Fus}\), \(\cat[n-k-2]{Rep}\)
\end{document}

Answer 1

This checks if + or - is in the argument.

\documentclass{article}
\usepackage{amsmath}
\usepackage{xparse}

\ExplSyntaxOn
\NewDocumentCommand{\cat}{om}
 {
  \IfValueT{#1}{ \is_cat_prefix:n { #1 } }
  \mathbf{#2}
 }

\cs_new_protected:Nn \is_cat_prefix:n
 {
  \str_if_in:nnTF { #1 } { + }
   { (#1) } % there is +
   {
    \str_if_in:nnTF { #1 } { - }
     { (#1) } % there is -
     { #1 }
   }
 }
\ExplSyntaxOff


\begin{document}

\(\cat{Bord}\), \(\cat[n]{Fus}\), \(\cat[2]{Rep}\), \(\cat[n+1]{Fus}\), \(\cat[n-k-2]{Rep}\)

\end{document}

Answer 2

I use listofitems here to check for the literal presence of + or - in argument #1 (others can be added).

\documentclass{article}
\usepackage{listofitems}
\newcommand{\cat}[2][\relax]{%
  \setsepchar{+||-}%
  \readlist\checksgns{#1}%
  \ifnum\listlen\checksgns[]>1\relax(#1)\else#1\fi\mathbf{#2}}
\begin{document}
    \(\cat{Bord}\), \(\cat[n]{Fus}\), \(\cat[2]{Rep}\), \(\cat[n+1]{Fus}\), \(\cat[n-k-2]{Rep}\)
\end{document}