Codensity and Stone spaces

Andrei Sipos

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arXiv · 1409.1370

Codensity and Stone spaces

Andrei Sipos

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Abstract

We present a detailed computation of two codensity monads associated to two canonical functors -- the inclusion functor of FinSet into Top and the inclusion functor of the category of the powers of the Sierpinski space into Top. We show that the essential images of the two monads are the categories of Stone spaces and of sober spaces, respectively. A new motivation for defining these classes of spaces is therefore obtained.

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Andrei Sipos. 2014-09-04. Codensity and Stone spaces. https://arxiv.org/abs/1409.1370

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