Coherence for indexed symmetric monoidal categories

Abstract

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.

If looking for the results of this paper in context of parameterized spectra please see arXiv:2306.03817 instead

References in corpus (3)

• Iterated spans and classical topological field theories
• Quasistrict symmetric monoidal 2-categories via wire diagrams
• Duality and traces for indexed monoidal categories

Cited by in corpus (1)

• $K$-theory of endomorphisms, the $TR$-trace, and zeta functions