  Indexed symmetric monoidal categories are an important refinement of
bicategories -- this structure underlies several familiar bicategories,
including the homotopy bicategory of parametrized spectra, and its equivariant
and fiberwise generalizations.
  In this paper, we extend existing coherence theorems to the setting of
indexed symmetric monoidal categories. The most central theorem states that a
large family of operations on a bicategory defined from an indexed symmetric
monoidal category are all canonically isomorphic. As a part of this theorem, we
introduce a rigorous graphical calculus that specifies when two such operations
admit a canonical isomorphism.
