# 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…

## 2 Citations

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It is often stated that Frobenius quantales are necessarily unital. By taking negation as a primitive operation, we can define Frobenius quantales that may not have a unit. We develop the elementary…

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