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Injective objects and retracts of Fraïssé limits

Injective objects and retracts of Fraïssé limits Abstract We present a purely category-theoretic characterization of retracts of Fraïssé 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 Fraïssé 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

Injective objects and retracts of Fraïssé limits

Forum Mathematicum , Volume 27 (2) – Mar 1, 2015

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References (35)

Publisher
de Gruyter
Copyright
Copyright © 2015 by the
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/forum-2012-0081
Publisher site
See Article on Publisher Site

Abstract

Abstract We present a purely category-theoretic characterization of retracts of Fraïssé 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 Fraïssé 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.

Journal

Forum Mathematicumde Gruyter

Published: Mar 1, 2015

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