Coherence for Monoidal Monads and Comonads

Details Coherence for Monoidal Monads and Comonads Coherence for Monoidal Monads and Comonads

2009-07-13

arxiv.org/abs/0907.2199v3

Mathematics

Category Theory

18 pages

Scientific paper

The goal of this paper is to prove coherence results with respect to relational graphs for monoidal monads and comonads, i.e. 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 axiomatize a plausible notion of identity of deductions in a fragment of the modal logic S4.

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