Homset

In a category, a hom-set is the type of all morphisms between two fixed objects.

$$\begin{array}{rl}& \text{Given category }\mathcal{C}:\mathbf{Set}\\ & \text{Given }a,b:\mathcal{C}\\ & \mathcal{C}[a,b]:\mathrm{Set}\end{array}$$