Year: 2012
Type: preprint
Abstract: This paper introduces an endofunctor $\VT$ on the category of frames, parametrized by an endofunctor $\T$ on the category $\Set$ that satisfies certain constraints. This generalizes Johnstone's construction of the Vietoris powerlocale, in the sense that his construction is obtained by taking for $\T$ the finite covariant power set functor. Our construction of the $\T$-powerlocale $\VT \bbL$ out of a frame $\bbL$ is based on ideas from coalgebraic logic and makes explicit the connection between the Vietoris construction and Moss's coalgebraic cover modality. We show how to extend certain natural transformations between set functors to natural transformations between $\T$-powerlocale functors. Finally, we prove that the operation $\VT$ preserves some properties of frames, such as regularity, zero-dimensionality, and the combination of zero-dimensionality and compactness.
Source: arXiv (Cornell University)
Authors: Venema, Yde, Vickers, Steve, Vosmaer, Jacob
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2951973246