Authors: Došen, Kosta 
Petrić, Zoran 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Coherence for monoidal monads and comonads
Journal: Mathematical Structures in Computer Science
Volume: 20
Issue: 4
First page: 545
Last page: 561
Issue Date: 1-Aug-2010
Rank: M23
ISSN: 0960-1295
DOI: 10.1017/S0960129510000034
The goal of this paper is to prove coherence results with respect to relational graphs for monoidal monads and comonads, that is, monads and comonads in a monoidal category such that the endofunctor of the monad or comonad is a monoidal functor (this means that it preserves 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. The monoidal structure is also allowed to be given with finite products or finite coproducts. Monoidal comonads with finite products axiomatise a plausible notion of equality of deductions in a fragment of the modal logic S4.
Publisher: Cambridge University Press
Project: Ministry of Science of Serbia (Grants 144013 and 144029)

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