Dualizing sup-preserving endomaps of a complete lattice

@inproceedings{Santocanale2021DualizingSE,
  title={Dualizing sup-preserving endomaps of a complete lattice},
  author={Luigi Santocanale},
  booktitle={ACT},
  year={2021}
}
It is argued in [5] that the quantale [L,L]∨ of sup-preserving endomaps of a complete lattice L is a Girard quantale exactly when L is completely distributive. We have argued in [16] that this Girard quantale structure arises from the dual quantale of inf-preserving endomaps of L via Raney’s transforms and extends to a Girard quantaloid structure on the full subcategory of SLatt (the category of complete lattices and sup-preserving maps) whose objects are the completely distributive lattices… 

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