2018/11/30 by Cary Malkiewich, Malkiewich, Cary, Kate Ponto +1
Mathematics · #18D05 #18D10 #18D30 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1811.12873
openalex publication_date 2018/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.