What is "slice category"

n. (context category theory English) Given a category ''C'' and an object ''X'' ∈ Ob(''C''), the ''slice category'' $C\; downarrow\; X$ has, as its objects, morphisms from objects of ''C'' to ''X'', and as its morphisms, morphisms connecting the tails of its own objects in a commutative way (i.e., closed under composition). The category $C\; downarrow\; X$ is said to be "over ''X''". (More formally, the objects of ''C'' over ''X'' are ordered pairs of the form (''A'', ''f'') where ''A'' is an object of ''C'' and ''f'' is a morphism from ''A'' to ''X''. Then the morphisms of ''C'' over ''X'' have such ordered pairs as their domains/codomains instead of objects of ''C'' directly.)