Quantaloid

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:

${\displaystyle (\bigvee _{i}f_{i})\circ (\bigvee _{j}g_{j})=\bigvee _{i,j}(f_{i}\circ g_{j})}$

The endomorphism lattice ${\displaystyle \mathrm {Hom} (X,X)}$ of any object ${\displaystyle X}$ in a quantaloid is a quantale, whence the name.

References

This category theory-related article is a stub. You can help Wikipedia by expanding it.

• v
• t
• e

This page was last edited on 27 January 2022, at 20:35