Fusion closure of transparent anyons
= Fusion closure of transparent anyons
For <transparent anyons> $a,b$, the <hexagon identities for braiding> for <braiding> express double exchange of $a\otimes b$ with any charge $x$ as the successive double exchanges of $a$ and $b$ with $x$. Both are identities. Naturality restricts the resulting identity to every simple <anyon fusion> summand $c$ of $a\otimes b$, proving that $c$ is transparent.