21 citations · 37 across the 30 of their papers we have counts for
34 papers
Lifting star-autonomous structures
Luigi Santocanale, Cédric de Lacroix, Gregory Chichery
For a functor from a category to the category of ordered sets and order-preserving functions, we study liftings of various kind of structures from the base category $…
Frobenius structures in star-autonomous categories
Luigi Santocanale, Cédric de Lacroix
It is known that the quantale of sup-preserving maps from a complete lattice to itself is a Frobenius quantale if and only if the lattice is completely distributive. Since complete…
Unitless Frobenius quantales
Cédric de Lacroix, Luigi Santocanale
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 deve…
Bijective proofs for Eulerian numbers of types B and D
Luigi Santocanale
Let $\Bigl\langle\matrix{n\cr k}\Bigr\rangle$, $\Bigl\langle\matrix{B_n\cr k}\Bigr\rangle$, and $\Bigl\langle\matrix{D_n\cr k}\Bigr\rangle$ be the Eulerian numbers in the types A,…
Dualizing sup-preserving endomaps of a complete lattice
Luigi Santocanale
It is argued in (Eklund et al., 2018) 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…
The Involutive Quantaloid of Completely Distributive Lattices
Luigi Santocanale
Let L be a complete lattice and let Q(L) be the unital quantale of join-continuous endo-functions of L. We prove the following result: Q(L) is an involutive (that is, non-commutati…