Homset

In category theory a so-called homset is the type of arrows between two objects:

$$\begin{array}{rl}& \text{Given category }\mathcal{C}:\mathbf{Set}\\ & \text{Given }A,B:\mathcal{C}\\ & \mathcal{C}[A,B]=\{f:arr(\mathcal{C}).dom(f)=A\wedge dom(f)=B\}\end{array}$$

Duplicate Content 1

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

Written $\mathcal{C}[a,b]$, $\mathrm{Hom}[a,b]$, $a{\to }_{\mathcal{C}}b$.