Reflexive, Symmetric, Transitive, &c

Injection, Surjection, Bijection

Domain and Range

Monad, Monoid, &c

...what others do I have to stop and think about often?

alaric added on 2013-08-02 09:49:14 UTC:
See https://en.wikipedia.org/wiki/Binary_relation#Relations_over_a_set for the relation types set.

Mention "argument" and "image" as part of the domain/range diagram.

Function types: bijection, injection, surjection, projection; defined in terms of orthogonal boolean flags - surjective and bijective.