Over (Cateogry)

Given a category $\mathcal{C}$ with object $a$, then the over category $\mathcal{C}/a$ is the category made of:

• objects are $(b,f):\Sigma b:\mathcal{C}.\mathrm{Hom}[b,a]$
• morphisms are $h:(b,f)\to (c,g)$ where $h:b\to c$ s.t. $g\circ h=f$.