Problem Calculus: Some Terminology

We're going to be using Spaces and Arrows to form the problem calculus diagrams.  Let's look at some basic definitions.

Given an arrow there is a Source space and a Destination space that can be thought of as the type of the inputs and the type of the outputs of the arrow.  Similarly, the arrow might only accept a subset of the objects in the Source space and produce a subset of the objects in the Destination space.  The subsets are called the Input space and Output space, respectively.