## Sets

Next: Monoidal Category Up: Appendix Previous: Appendix

# Sets

Definition 2.1   a pre-ordered set is a set with the property that, between any two objects, there is at most one arrow. This entails that there exists a binary relation R between the objects of the pre-ordered set, such that the following holds:
1. aRa (reflexivity)
2. if aRb and bRc then aRc (transitivity)

Definition 2.2:   a poset is a pre-ordered set with the extra property of being antisymmetric: $pRq\hspace{.2in}and\hspace{.2in}qRp\hspace{.2in}\Rightarrow p=q$

Cecilia Flori 2006-11-19