Authors: Došen, Kosta 
Petrić, Zoran 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Coherence for monoidal endofunctors
Journal: Mathematical Structures in Computer Science
Volume: 20
Issue: 4
First page: 523
Last page: 543
Issue Date: 1-Aug-2010
Rank: M23
ISSN: 0960-1295
DOI: 10.1017/S0960129510000022
Abstract: 
The goal of this paper is to prove coherence results with respect to relational graphs for monoidal endofunctors, that is, 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.
Publisher: Cambridge University Press
Project: Ministry of Science of Serbia (Grants 144013 and 144029)

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