What is "quantaloid"

In mathematics, a quantaloid is a category enriched over the category Sup of suplattices. In other words for any objects a, b the morphism object between them is not just a set but a complete lattice, in such a way that composition of morphisms preserves all joins:

(⋁f) ∘ (⋁g) = ⋁(f ∘ g)

The endomorphism lattice Hom(X, X) of any object X in a quantaloid is a quantale, whence the name.