Codensity and Stone spaces

Year, pages: 2018, 57 - 70

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 Sierpiński space into $\Top$. We show that the categories of algebras 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.

Sipos, A. 2018. Codensity and Stone spaces. In Mathematica Slovaca, vol. 68, no.1, pp. 57-70. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0080

Sipos, A. (2018). Codensity and Stone spaces. Mathematica Slovaca, 68(1), 57-70. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0080