What is the meaning of Direct_limit?

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 $i\leq k,\ j\leq k$ 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 $f_{jj}(a_{j})=a_{j},\ f_{ij}(a_{i})=a_{j}$ .)

a colimit

Source: wiktionary.org

What is the meaning of Direct_limit?

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