Overcategory

In mathematics, specifically category theory, an overcategory (and undercategory) is a distinguished class of categories used in multiple contexts, such as with covering spaces (espace etale). They were introduced as a mechanism for keeping track of data surrounding a fixed object ${\displaystyle X}$ in some category ${\displaystyle {\mathcal {C}}}$. There is a dual notion of undercategory, which is defined similarly.