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.

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

References in corpus (4)

• A proof of uniqueness of the Gurarii space
• Banach spaces of universal disposition
• The Bergman property for endomorphism monoids of some Fra\"ıssé limits
• A note on ANR's

Cited by in corpus (5)

• Operator space and operator system analogs of Kirchberg's nuclear embedding theorem
• On automatic homeomorphicity for transformation monoids
• Universal homomorphisms, universal structures, and the polymorphism clones of homogeneous structures
• 1-complemented subspaces of Banach spaces of universal disposition
• Polymorphism clones of homogeneous structures (Universal homogeneous polymorphisms and automatic homeomorphicity)