泛同态、泛结构和齐次结构的多态克隆
Universal homomorphisms, universal structures, and the polymorphism clones of homogeneous structures
摘要：
利用Droste和Göbel的Fraïssé定理的范畴版本，我们导出了一个逗号范畴具有泛齐次对象的准则。作为第一个应用，我们给出了泛结构和ω-范畴泛结构的新的存在性结果。作为第二个应用程序，我们刻画了一大类均匀结构的回缩，扩展了Bonato，Delić，Dolinka和Kubietan以前的结果。作为第三个应用程序，我们证明了一个大类的同质结构，其多态性克隆所产生的多态性的有界arity，推广了一个经典的结果Sierpienski克隆的所有功能在一个给定的集合是由其二进制部分。进一步研究了克隆的共尾性和Bergman性质，给出了同构上存在具有不可数共尾性和Bergman性质的多态克隆的充分条件.
英文摘要：
Using a categorial version of Fraïssé's theorem due to Droste and Göbel, we derive a criterion for a comma-category to have universal homogeneous objects. As a first application we give new existence result for universal structures and for ω-categorical universal structures. As a second application we characterize the retracts of a large class of homogeneous structures, extending previous results by Bonato, Delić, Dolinka, and Kubiś. As a third application we show for a large class of homogeneous structures that their polymorphism clone is generated by polymorphisms of bounded arity, generalizing a classical result by Sierpiński that the clone of all functions on a given set is generated by its binary part. Further we study the cofinality and the Bergman property for clones and we give sufficient conditions on a homogeneous structure to have a polymorphism clone that has uncountable cofinality and the Bergman property.
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