  Dagger categories are an essential tool for categorical descriptions of
quantum physics, but pose a challenge to category theorists as their definition
is in tension with the ``principle of equivalence'' that lies at the heart of
category theory.
  In this note we propose the alternative, coherent definition of an
``involutive category with a notion of positivity'' and show that the
$2$-category formed by these is biequivalent to the $2$-category of dagger
categories.
