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In mathematics, a quantaloid is a category enriched over the category Sup of suplattices.[1] 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:

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


  1. ^ Rosenthal, Kimmo I. (1996), The theory of quantaloids, Pitman Research Notes in Mathematics Series, 348, Longman, Harlow, ISBN 0-582-29440-1, MR 1427263 . See in particular p. 15.