Retracts of ultrahomogeneous structures in the context of Katětov functors. (English) Zbl 1347.03067
Summary: In this paper, we characterize retracts of a wide class of Fraïssé limits using the tools developed in a recent paper by W. Kubiś and the present author [“Katetov functors”, Preprint, arXiv:1412.1850], which we refer to as Katětov functors. This approach enables us to conclude that in many cases, a structure is a retract of a Fraïssé limit if and only if it is algebraically closed in the surrounding category.
References:
| [1] | I. Ben Yaacov, The linear isometry group of the Gurarij space is universal. arXiv:1203. 4915v4.; · Zbl 1311.46004 |
| [2] | D. Bilge, J. Melleray, Elements of finite order in automorphism groups of homogeneous structures, Contrib. Discret. Math. 8 (2013), 88-119.; · Zbl 1321.20003 |
| [3] | P. J. Cameron, J. Nešetril, Homomorphism-homogeneous relational structures, Combin. Probab. Comput. 15 (2006), 91-103.; · Zbl 1091.08001 |
| [4] | I. Dolinka, A characterization of retracts in certain Fraíssé limits, Math. Log. Q. 58 (2012), 46-54.; · Zbl 1247.03046 |
| [5] | R. Fraïssé, Sur certains relations qui généralisent l’ordre des nombres rationnels, C. R. Acad. Sci. Paris 237 (1953), 540-542.; · Zbl 0051.03803 |
| [6] | M. Katétov, On universal metric spaces. General topology and its relations to modern analysis and algebra, VI (Prague, 1986), Res. Exp. Math., vol. 16, Heldermann, Berlin, 1988, 323-330.; · Zbl 0642.54021 |
| [7] | W. Kubis, Injective objects and retracts of Fraïssé limits, Forum Math. 27 (2013), 807-842.; · Zbl 1348.18003 |
| [8] | W. Kubis, D. Mašulovic, Katetov functors. arXiv:1412.1850v2.; |
| [9] | P. S. Urysohn, Sur un espace métrique universel, Bull. Math. Sci. 51 (1927), 43-64, 74-90.; · JFM 53.0556.01 |
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