Some aspects of (non) functoriality of natural discrete covers of locales

@article{Ball2019SomeAO,
  title={Some aspects of (non) functoriality of natural discrete covers of locales},
  author={R. Ball and J. Picado and A. Pultr},
  journal={Quaestiones Mathematicae},
  year={2019},
  volume={42},
  pages={701 - 715}
}
Abstract The frame Sc(L) generated by closed sublocales of a locale L is known to be a natural Boolean (“discrete”) extension of a subfit L; also it is known to be its maximal essential extension. In this paper we first show that it is an essential extension of any L and that the maximal essential extensions of L and Sc(L) are isomorphic. The construction Sc is not functorial; this leads to the question of individual liftings of homomorphisms L → M to homomorphisms Sc(L) → Sc(M). This is… Expand
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