ind-object：インド象？ｗ（＾＾ https://ncatlab.org/nlab/show/ind-object nLab ind-object Last revised on April 12, 2018 Contents 1. Idea 2. Definition As diagrams As filtered colimits of representable presheaves 3. Examples 4. Properties The category of ind-objects Recognition of Ind-objects Functoriality The case that C already admits filtered colimits 5. Applications 6. In higher category theory In (∞,1)-categories 7. Related concepts 8. References (抜粋) 1. Idea An ind-object of a category C is a formal filtered colimit of objects of C. Here “formal” means that the colimit is taken in the category of presheaves of C (the free cocompletion of C). The category of ind-objects of C is written ind-C or Ind(C). Here, “ind” is short for “inductive system”, as in the inductive systems used to define directed colimits, and as contrasted with “pro” in the dual notion of pro-object corresponding to “projective system”.
