definition. slice category [kostecki2011introduction, eq. 12] [tt-0009]
The slice category \({\cal C} \downarrow X\), is the category whose objects are arrows in \({\cal C}\) with fixed codomain \(X\), such that the diagram
definition. slice category [kostecki2011introduction, eq. 12] [tt-0009]
commutes, where colored arrows are in \({\cal C} \downarrow X\).
It's also denoted \({\cal C} / X\) or \({\cal C}_{/X}\).
The slice category is a special case of the comma category.
It's also called overcategory, as it's a slice category over \(X\) [zhang2021type, 3.5].
revamp and add co-slice category, maybe following [rosiak2022sheaf, def. 21], or better, follow Basic category theory, to explain how a slice category is a special case of comma category.