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A non-commutative Priestley duality |
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| Authors: | Andrej Bauer Karin Cvetko-Vah Mai Gehrke Samuel J. van Gool Ganna Kudryavtseva |
| Affiliation: | 1. University of Ljubljana, Faculty of Mathematics and Physics, Jadranska 19, SI-1001, Ljubljana, Slovenia;2. LIAFA, CNRS and Université Paris Diderot – Paris 7, Case 7014, F-75205, Paris Cedex 13, France;3. IMAPP, Radboud University Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands;4. University of Ljubljana, Faculty of Computer and Information Science, Tr?aška cesta 25, SI-1001, Ljubljana, Slovenia |
| Abstract: | We prove that the category of left-handed strongly distributive skew lattices with zero and proper homomorphisms is dually equivalent to a category of sheaves over local Priestley spaces. Our result thus provides a non-commutative version of classical Priestley duality for distributive lattices and generalizes the recent development of Stone duality for skew Boolean algebras. |
| Keywords: | 06D50 06F05 54B40 |
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