Dualizing sup-preserving endomaps of a complete lattice

@inproceedings{Santocanale2020DualizingSE,
  title={Dualizing sup-preserving endomaps of a complete lattice},
  author={L. Santocanale},
  booktitle={ACT},
  year={2020}
}
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… Expand

References

SHOWING 1-10 OF 20 REFERENCES
Tight Galois connections and complete distributivity
Feedback for linearly distributive categories: traces and fixpoints
Proof theory for full intuitionistic linear logic, bilinear logic, and MIX categories.
Natural deduction and coherence for weakly distributive categories
The continuous weak order
Nuclearity in the category of complete semilattices
Coherence for compact closed categories
A New Lattice Construction: The Box Product
Tensorial decomposition of concept lattices
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