direct limit

Meaning

Noun

• 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 $i\; \backslash le\; k,\; \backslash \; j\; \backslash le\; k$ in the indexing poset, then there exist $f\_\{ik\}:A\_i\; \backslash rightarrow\; A\_k$ and $f\_\{jk\}:A\_j\backslash rightarrow\; A\_k$. If $a\_i\; \backslash in\; A\_i,\; \backslash \; a\_j\; \backslash in\; A\_j$ such that $f\_\{ik\}(a\_i)\; =\; f\_\{jk\}(a\_j)$ then $a\_i\; \backslash sim\; a\_j$. If k = j then $f\_\{jj\}(a\_j)\; =\; a\_j,\; \backslash \; f\_\{ij\}(a\_i)\; =\; a\_j$.)
• a colimit

Related

Similar words

• inductive limit

Opposite words

• inverse limit