Want to be able to answer questions about resources like:
Given what I have, is it possible to get what I want?
Given what I have, what is the minimum cost to get what I want?
Given what I have, what is the set of ways to get what I want?
Monoidal preorders will allow us to build new recipes from old ones.
Resources are not always consumed when used.
A \(\mathcal{V}\) category is a set of objects, which one may think of as points on a map
\(\mathcal{V}\) somehow ’structures the question’ of getting from point a to b
\(\mathcal{V} = Bool\) answers the question of whether we can get to b
\(\mathcal{V} = Cost\) can help answer how to get to b with minimum cost.
\(\mathcal{V} = \mathbf{Set}\) can yield a set of methods to get to b.