Codensity and Stone spaces

In: Mathematica Slovaca, vol. 68, no. 1

Andrei Sipos

Detaily:

Rok, strany: 2018, 57 - 70

Kľúčové slová:

codensity, monad, ultrafilter, Stone space, frame, sober space

DOI: https://doi.org/10.1515/ms-2017-0080

O článku:

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.

Ako citovať:

ISO 690:

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

APA:

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

O vydaní:

Publikované: 23. 2. 2018