Quantaloid

From HandWiki

In mathematics, a quantaloid is a category enriched over the category Sup of suplattices.[1] In other words, for any objects a and 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:

(ifi)(jgj)=i,j(figj)

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

References

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