  Markov categories have recently emerged as a powerful high-level framework
for probability theory and theoretical statistics. Here we study a quantum
version of this concept, called involutive Markov categories. First, we show
that these are equivalent to Parzygnat's quantum Markov categories but argue
that they are simpler to work with. Our main examples of involutive Markov
categories involve C*-algebras (of any dimension) as objects and completely
positive unital maps as morphisms in the picture of interest. Second, we prove
a quantum de Finetti theorem for both the minimal and the maximal C*-tensor
norms, and we develop a categorical description of such quantum de Finetti
theorems which amounts to a universal property of state spaces.
