2009/07/13 by Kosta Došen, K. Dosen, Dosen, K. +3
Computer Science · Mathematics · #03F05 #03F07 #18A15 #18C05 #18D10 #Advanced Topics in Algebra #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Logic, programming, and type systems #math.CT #math.LO #msc:03F05 #msc:03F07 #msc:18A15 #msc:18C05 #msc:18D10
paper · pdf · doi:10.48550/arxiv.0907.2194
22 pages, minor corrections
openalex publication_date 2009/07/13 · arxiv created 2010/01/08 · arxiv updated 2010/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The goal of this paper is to prove coherence results with respect to relational graphs for monoidal endofunctors, i.e. endofunctors of a monoidal category that preserve the monoidal structure up to a natural transformation that need not be an isomorphism. These results are proved first in the absence of symmetry in the monoidal structure, and then with this symmetry. In the later parts of the paper the coherence results are extended to monoidal endofunctors in monoidal categories that have diagonal or codiagonal natural transformations, or where the monoidal structure is given by finite products or coproducts. Monoidal endofunctors are interesting because they stand behind monoidal monads and comonads, for which coherence will be proved in a sequel to this paper.