regular values of PL maps In the category of smooth manifolds and maps, $y$ is a regular value of $f$ iff the tangent map $df(x)$ is surjective for any $x\in f^{-1}(y)$. Then the preimage $f^{-1}(y)$ is a smooth submanifold. What is the analogical definition in the category of PL manifolds and PL maps? Some natural definition of "regular values" such that, for a regular value $y$, $f^{-1}(y)$ is a PL submanifold?

This should be in Rourke and Sanderson's book "Introduction to PL topology". Also, take a look at this paper about PL transversality. Once you know what transversality means, if you have a PL map $f: M\to N$ between PL manifolds, then a point $p\in N$ is a regular value of $f$ iff $f$ is transversal to $\\{p\\}$.