**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:- aRa (reflexivity)
- if aRb and bRc then aRc (transitivity)

**Definition 2.2:**

*a*

**poset**is a pre-ordered set with the extra property of being antisymmetric:

Cecilia Flori 2006-11-19