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An example of a Fraïssé class without a Katětov functor. (English) Zbl 1459.03044

Summary: We disprove a conjecture from W. Kubiś and D. Mašulović [Appl. Categ. Struct. 25, No. 4, 569–602 (2017; Zbl 1423.03125)] by showing the existence of a Fraïssé class \(\mathcal {C}\) which does not admit a Katětov functor. On the other hand, we show that the automorphism group of the Fraïssé limit of \(\mathcal {C}\) is universal, as it happens in the presence of a Katětov functor.

MSC:

03C50 Models with special properties (saturated, rigid, etc.)
18A22 Special properties of functors (faithful, full, etc.)

Citations:

Zbl 1423.03125
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References:

[1] Hodges, W.: Model theory, Encyclopedia of Mathematics and its Applications, vol. 42. Cambridge University Press, Cambridge (1993) · Zbl 1423.03125
[2] Kubiś, W., Mašulović, D.: Katĕtov Functors. Appl. Categor. Struct. (2016). doi:10.1007/s10485-016-9461-z · Zbl 1423.03125 · doi:10.1007/s10485-016-9461-z
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