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Coherence for monoidal monads and comonads†

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

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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.

Information

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 20 , Issue 4 , August 2010 , pp. 545 - 561
Copyright
Copyright © Cambridge University Press 2010

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