Examples Topological limits. Limits of functions are a special case of limits of filters, which are related to categorical limits as follows. Given a topological space X, denote by F the set of filters on X, x ∈ X a point, V(x) ∈ F the neighborhood filter of x, A ∈ F a particular filter and F_{x,A}={G∈ F｜ V(x)∪A ⊂ G}the set of filters finer than A and that converge to x. The filters F are given a small and thin category structure by adding an arrow A → B if and only if A ⊆ B. The injection I_{x,A}:F_{x,A}→ F becomes a functor and the following equivalence holds : x is a topological limit of A if and only if A is a categorical limit of I_{x,A} (引用終り) 以上
