Overcategory

In mathematics, an overcategory (also called a slice category) is a construction from category theory used in multiple contexts, such as with covering spaces (espace étalé). They were introduced as a mechanism for keeping track of data surrounding a fixed object ${\displaystyle X}$ in some category ${\displaystyle {\mathcal {C}}}$. The dual notion is that of an undercategory (also called a coslice category).