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Locales

Locales, frames, coframes, meet semi-lattices of locally closed subsets, and Boolean algebras of constructible sets

2024.05-01

4 May 2024

Mohamed Barakat
Email: mohamed.barakat@uni-siegen.de
Homepage: https://mohamed-barakat.github.io
Address:
Walter-Flex-Str. 3
57068 Siegen
Germany

Markus Lange-Hegermann
Email: markus.lange-hegermann@th-owl.de
Homepage: https://www.th-owl.de/eecs/fachbereich/team/markus-lange-hegermann/
Address:
Markus Lange-Hegermann
Hochschule Ostwestfalen-Lippe
Liebigstra├če 87
32657 Lemgo
Germany

Tom Kuhmichel
Email: tom.kuhmichel@student.uni-siegen.de
Homepage: https://github.com/TKuh
Address:
Walter-Flex-Str. 3
57068 Siegen
Germany

Contents

1 Prosets (preordered sets)
2 Posets (partially ordered sets)
3 Lattices
4 Heyting algebras
5 Co-Heyting algebras
6 Boolean algebras
7 Preordered sets viewed as categories
8 The (stable) proset/poset of a category
9 Meet-semilattice of single/multiple differences
10 Meet-semilattice of differences
11 Meet-semilattice of multiple differences
12 Boolean algebra of constructible objects
13 The interval category
14 Tools
15 Tests
16 Locales automatic generated documentation
Index

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