TL;DR
This paper proves that the category of locales is rigid, meaning every endo-equivalence is essentially the identity, by establishing new results on automorphisms and order-preserving properties of frames.
Contribution
It introduces novel results on automorphisms and order-preserving properties to demonstrate the rigidity of the category of locales.
Findings
Every endo-equivalence on the category of locales is isomorphic to the identity
New bounds on automorphisms between frames
Order-preserving properties of endo-equivalences
Abstract
In this paper we show that the category of frames, and, thus, the cate- gory of locales is 'rigid'. This means that every endo-equivalence on them is isomorphic to the identity functor. To reach this result we prove new results concerning the number of automorphisms between frames and new results concerning the order preserving properties of endo-equivalences.
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Taxonomy
TopicsRings, Modules, and Algebras · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology