A Categorical Construction of Ultrafilters

Details A Categorical Construction of Ultrafilters A Categorical Construction of Ultrafilters

2007-10-12

arxiv.org/abs/0710.2497v2

Mathematics

Category Theory

5 pages

Scientific paper

Ultrafilters are useful mathematical objects having applications in nonstandard analysis, Ramsey theory, Boolean algebra, topology, and other areas of mathematics. In this note, we provide a categorical construction of ultrafilters in terms of the inverse limit of an inverse family of finite partitions; this is an elementary and intuitive presentation of a consequence of the profiniteness of Stone spaces. We then apply this construction to answer a question of Rosinger posed in arXiv:0709.0084v2 in the negative.

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