direct limit

Noun

 * 1)  A set of equivalence classes which partition the disjoint union of the members of a direct system; each equivalence class being a sort of “drainage basin” of the mappings (of the morphisms) of the direct system, if these are analogically considered as “rivers”. (If $$i \le k, \ j \le k$$ in the indexing poset, then there exist $$f_{ik}:A_i \rightarrow A_k$$ and $$f_{jk}:A_j\rightarrow A_k$$. If $$a_i \in A_i, \ a_j \in A_j$$ such that $$f_{ik}(a_i) = f_{jk}(a_j)$$ then $$a_i \sim a_j$$. If k = j then $$f_{jj}(a_j) = a_j, \ f_{ij}(a_i) = a_j$$.)
 * 2)  a colimit
 * 1)  a colimit
 * 1)  a colimit