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June 2017 Equilogical spaces and algebras for a double-power monad
Giulia Frosoni, Giuseppe Rosolini
Tbilisi Math. J. 10(3): 121-139 (June 2017). DOI: 10.1515/tmj-2017-0105

Abstract

We investigate the algebras for the double-power monad on the Sierpisnki space in the category $\mathcal{Equ}$ of equilogical spaces, a cartesian closed extension of $\mathcal{Top}_0$ introduced by Scott, and the relationship of such algebras with frames. In particular, we focus our attention on interesting subcategories of $\mathcal{Equ}$. We prove uniqueness of the algebraic structure for a large class of equilogical spaces, and we characterize the algebras for the double-power monad in the category of algebraic lattices and in the category of continuous lattices, seen as full subcategories of $\mathcal{Equ}$.

We also analyse the case of algebras in the category $\mathcal{Top}_0$ of $\mathrm{T}_0$-spaces, again seen as a full subcategoy of $\mathcal{Equ}$, proving that each algebra for the double-power monad in $\mathcal{Top}_0$ has an underlying sober, compact, connected space.

Citation

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Giulia Frosoni. Giuseppe Rosolini. "Equilogical spaces and algebras for a double-power monad." Tbilisi Math. J. 10 (3) 121 - 139, June 2017. https://doi.org/10.1515/tmj-2017-0105

Information

Received: 25 September 2017; Revised: 19 October 2017; Published: June 2017
First available in Project Euclid: 20 April 2018

zbMATH: 06816532
MathSciNet: MR3724482
Digital Object Identifier: 10.1515/tmj-2017-0105

Rights: Copyright © 2017 Tbilisi Centre for Mathematical Sciences

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Vol.10 • No. 3 • June 2017
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