In mathematics, a quantaloid is a

category Category, plural categories, may refer to: Philosophy and general uses *Categorization, categories in cognitive science, information science and generally * Category of being * ''Categories'' (Aristotle) * Category (Kant) * Categories (Peirce) ...

enriched over the category Sup of '' suplattices''.. See in particula
p. 15
In other words, for any objects ''a'' and ''b'' the morphism object between them is not just a set but a complete

lattice Lattice may refer to: Arts and design * Latticework, an ornamental criss-crossed framework, an arrangement of crossing laths or other thin strips of material * Lattice (music), an organized grid model of pitch ratios * Lattice (pastry), an orna ...

, in such a way that composition of morphisms preserves all joins: :

(\bigvee_i f_i) \circ (\bigvee_j g_j) = \bigvee_ (f_i \circ g_j)

The

endomorphism In mathematics, an endomorphism is a morphism from a mathematical object to itself. An endomorphism that is also an isomorphism is an automorphism. For example, an endomorphism of a vector space is a linear map , and an endomorphism of a gr ...

lattice

\mathrm(X,X)

of any object

X

in a quantaloid is a quantale, whence the name.

References

Category theory {{Cattheory-stub