Quantaloid
≈ 1 min read
Names in other languages
No names in other languages are held for this entry yet.
Article bodies are English and are not machine-translated. A name in another language is not a translation of the article.
In mathematics, a quantaloid is a category enriched over the category Sup of complete lattices with supremum-preserving maps. 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: : (\bigvee_i f_i) \circ (\bigvee_j g_j) = \bigvee_{i,j} (f_i \circ g_j) The endomorphism lattice \mathrm{Hom}(X,X) of any object X in a quantaloid is a quantale, whence the name.
In mathematics, a quantaloid is a category enriched over the category Sup of complete lattices with supremum-preserving maps. 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: (\bigvee_i f_i) \circ (\bigvee_j g_j) = \bigvee_{i,j} (f_i \circ g_j) The endomorphism lattice \mathrm{Hom}(X,X) of any object X in a quantaloid is a quantale, whence the name. ==References==
Text derived from https://en.wikipedia.org/w/index.php?oldid=1252050912 under CC BY-SA 4.0; modifications have been made.