Let $V$ be a finite dimensional vector space.
Let $U,W$ be subspaces of $V$.
Now
$$ \text{dim}(U \cap W) = \text{dim}(U) + \text{dim}(W) - \text{dim}(U + W). $$
What is the the category theory interpretation of that statement, seeing that it looks like the inclusion-exclusion principle
$$ \text{card}(U \cup W) = \text{card}(U) + \text{card}(W) - \text{card}(U \cap W) $$
where $U$ and $W$ are now sets, $\text{card}()$ stands for cardinality, and intersection has been replaced by the union and sum by intersection?
Looks like some functor from finite dimensional vector spaces to $\text{Set}$. Or something.