Injective objects and retracts of Fraïssé limits

Details Injective objects and retracts of Fraïssé limits Injective objects and retracts of Fraïssé limits

2011-07-22

arxiv.org/abs/1107.4620v2

Mathematics

Category Theory

28 pages; small corrections and more references added. Complete version

Scientific paper

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.

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