{{technical|date=September 2010}} In mathematics, a '''quantaloid''' is a category enriched over the category '''Sup''' of complete lattices with supremum-preserving maps.<ref>{{citation | last = Rosenthal | first = Kimmo I. | isbn = 0-582-29440-1 | mr = 1427263 | publisher = Longman, Harlow | series = Pitman Research Notes in Mathematics Series | title = The theory of quantaloids | volume = 348 | year = 1996}}. See in particular [https://books.google.com/books?id=O3bno8HpcFAC&pg=PA15 p. 15].</ref> In other words, for any objects ''a'' and ''b'' the Hom object between them is not just a set but a complete lattice, in such a way that composition of morphisms preserves all joins: :<math>(\bigvee_i f_i) \circ (\bigvee_j g_j) = \bigvee_{i,j} (f_i \circ g_j) </math>
The endomorphism lattice <math>\mathrm{Hom}(X,X)</math> of any object <math>X</math> in a quantaloid is a quantale, whence the name.
==References== {{reflist}}
Category:Category theory
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