English

Injective objects and retracts of Fra\"iss\'e limits

Category Theory 2013-10-10 v4 Logic

Abstract

We present a purely category-theoretic characterization of retracts of Fra\"iss\'e limits. For this aim, we consider a natural version of injectivity with respect to a pair of categories (a category and its subcategory). It turns out that retracts of Fra\"iss\'e limits are precisely the objects that are injective relatively to such a pair. One of the applications is a characterization of non-expansive retracts of Urysohn's universal metric space.

Keywords

Cite

@article{arxiv.1107.4620,
  title  = {Injective objects and retracts of Fra\"iss\'e limits},
  author = {Wieslaw Kubiś},
  journal= {arXiv preprint arXiv:1107.4620},
  year   = {2013}
}

Comments

33 pages; minor corrections; extended introduction and more references. Final version

R2 v1 2026-06-21T18:40:49.469Z