direct limit (English, noun)
expansion: direct limit (plural direct limits)
Senses:
topics: algebra
mathematics
sciences
glosses: 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<k,j<k in the indexing poset, then there exist f_ik:A_i→A_k and f_jk:A_j→A_k. If a_i∈A_i,a_j∈A_j such that f_ik(a_i)=f_jk(a_j) then a_i∼a_j. If k = j then f_jj(a_j)=a_j,f_ij(a_i)=a_j.)
topics: category-theory
computing
engineering
mathematics
natural-sciences
physical-sciences
sciences
glosses: a colimit
Forms:
form: direct limits
tags: plural