  The theory of shadows is an axiomatic, bicategorical framework that
generalizes topological Hochschild homology (THH) and satisfies analogous
important properties, such as Morita invariance. Using Berman's extension of
THH to bicategories, we prove that there is an equivalence between functors out
of Hochschild homology of a bicategory and shadows on that bicategory. As part
of that proof we give a computational description of pseudo-functors out of the
truncated simplex category and a variety thereof, which can be of independent
interest.
  Building on this result we present three applications: (1) We provide a new,
conceptual proof that shadows, and as a result the Euler characteristic and
trace introduced by Campbell and Ponto, are Morita invariant. (2) We strengthen
this result by using an explicit computation of the Hochschild homology of the
free adjunction bicategory to show that the construction of the Euler
characteristic is homotopically unique. (3) We generalize the construction of
$\mathscr{V}$-enriched Hochschild homology, where $\mathscr{V}$ is a
presentably symmetric monoidal $\infty$-category, to bimodules, and prove it
gives us a shadow.
