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Coherence for monoidal endofunctors†

Published online by Cambridge University Press:  27 May 2010

KOSTA DOŠEN  and
ZORAN PETRIĆ
KOSTA DOŠEN
Affiliation:
Mathematical Institute, SANU, Knez Mihailova 36, P.O. Box 367, 11001 Belgrade, Serbia Email: kosta@mi.sanu.ac.rs; zpetric@mi.sanu.ac.rs
ZORAN PETRIĆ
Affiliation:
Mathematical Institute, SANU, Knez Mihailova 36, P.O. Box 367, 11001 Belgrade, Serbia Email: kosta@mi.sanu.ac.rs; zpetric@mi.sanu.ac.rs
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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.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 20 , Issue 4 , August 2010 , pp. 523 - 543
Copyright
Copyright © Cambridge University Press 2010

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