Quantum topologists are used to think about traces
in the framework of spherical fusion categories, i.e.
in a two-dimensional context to which a two-dimensional
graphical calculus can be associated. We explain that traces
are already naturally defined for twisted endomorphisms of
linear categories, i.e. in a one-dimensional context.
For monoidal categories, the endomorphisms are twisted
by the Nakayama functor which is a twisted module functor
and hence an inherently three-dimensional object. This
naturally leads to a three-dimensional graphical calculus
which has natural applications to Turaev-Viro topological
field theories with defects.