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arXiv · 0710.2497

A Categorical Construction of Ultrafilters

Daniel Litt·Zachary Abel·Scott D. Kominers
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Abstract

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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Daniel Litt, Zachary Abel, Scott D. Kominers. 2009-05-13. A Categorical Construction of Ultrafilters. https://arxiv.org/abs/0710.2497

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