## Franklin's Notes

### Hom-set

In category theory , the hom-set between two objects $X$ and $Y$, denoted $\mathsf{C}(X,Y)$ or $\text{Hom}(X,Y)$, is the set of morphisms from $X$ to $Y$. This set only exists for all pairs of objects $X,Y$ in a category if the category is locally small, that is, if there is only "a set's worth of morphisms" between any pair of objects in the category.