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
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In other words, for any objects ''a'' and ''b'' the

morphism In mathematics, particularly in category theory, a morphism is a structure-preserving map from one mathematical structure to another one of the same type. The notion of morphism recurs in much of contemporary mathematics. In set theory, morphis ...

object between them is not just a set but a complete lattice, 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 ...

lattice

\mathrm(X,X)

of any object

X

in a quantaloid is a quantale, whence the name.

References

Category theory {{Cattheory-stub