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Universal objects in quasiconstructs

R. Rother (2000)

Commentationes Mathematicae Universitatis Carolinae

The general theory of J’onsson-classes is generalized to strongly smooth quasiconstructs in such a way that it also allows the construction of universal categories. One example of the theory is the existence of a concrete universal category over every base category. Properties are given which are (under certain conditions) equivalent to the existence of homogeneous universal objects. Thereby, we disprove the existence of a homogeneous C-universal category. The notion of homogeneity is strengthened...

Universality of separoids

Jaroslav Nešetřil, Ricardo Strausz (2006)

Archivum Mathematicum

A separoid is a symmetric relation 2 S 2 defined on disjoint pairs of subsets of a given set S such that it is closed as a filter in the canonical partial order induced by the inclusion (i.e., A B A ' B ' A A ' and B B ' ). We introduce the notion of homomorphism as a map which preserve the so-called “minimal Radon partitions” and show that separoids, endowed with these maps, admits an embedding from the category of all finite graphs. This proves that separoids constitute a countable universal partial order. Furthermore,...

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