Construction 7.45.

There are presentably symmetric monoidal categories \(n\Pr\) for all \(n\geq 0\), with

\[0\Pr = \An, \qquad 1\Pr = \Pr.\]

The construction is iterated by passing to presentable module categories. Throughout this section the relevant presentability cardinal is \(\aleph_1\), so that “presentable” means compatible with countable colimits. We suppress this cardinal from the notation.