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Injective objects and retracts of Fraïssé limits
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Wiesław Kubiś
Published/Copyright:
January 5, 2013
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.
Funding source: GAČR
Award Identifier / Grant number: P 201/12/0290
The author is indebted to the anonymous referee for several helpful remarks, in particular for pointing out the reference [`Endomorphisms of Fraïssé limits and automorphism groups of algebraically closed relational structures', PhD thesis, University of St Andrews, 2012].
Received: 2012-6-12
Revised: 2012-10-22
Published Online: 2013-1-5
Published in Print: 2015-3-1
© 2015 by De Gruyter
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Articles in the same Issue
- Frontmatter
- Near abelian profinite groups
- On Calabi–Yau threefolds associated to a web of quadrics
- On the partial fraction decomposition of the restricted partition generating function
- Projectively flat Finsler manifolds with infinite dimensional holonomy
- Weighted version of Carleson measure and multilinear Fourier multiplier
- Injective objects and retracts of Fraïssé limits
- On hypersurfaces containing projective varieties
- Additive reducts of algebraically closed valued fields
- On the subconvexity problem for GL(3) × GL(2) L-functions
- An algebraic property of Hecke operators and two indefinite theta series
- Sum formula of multiple Hurwitz-zeta values
- Classification of homogeneous holomorphic hermitian principal bundles over G/K
- Integrality properties of the CM-values of certain weak Maass forms
- Heat kernel for fractional diffusion operators with perturbations
- New class of multiple weights and new weighted inequalities for multilinear operators
- Balanced Hermitian geometry on 6-dimensional nilmanifolds
- Extensions of tame algebras and finite group schemes of domestic representation type
- Weighted estimates for multilinear Fourier multipliers
- Cluster tilting vs. weak cluster tilting in Dynkin type A infinity
- From ring epimorphisms to universal localisations
- Brauer algebras of type B
- Existence problems for the p-Laplacian
- Averaging operators over nondegenerate quadratic surfaces in finite fields
- Lawson homology for abelian varieties
