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.
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