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An adjunction between boolean algebras and a subcategory of Stone algebras
Theory and applications of categories, Tome 41 (2024), pp. 2041-2057

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We consider Stone algebras with a distinguished element e satisfying the identity e → x = ¬ ¬ x for all elements x of the algebra. We provide an adjunction between the category of such algebras and that of Boolean algebras. This adjunction turns out to involve the concept of assume-guarantee contracts, which has numerous applications throughout engineering and computer science.

Publié le :
Classification : 08A70, 08C05
Keywords: Stone algebras, contracts, assume-guarantee reasoning 
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     author = {Inigo Incer},
     title = {An adjunction between boolean algebras and a subcategory of {Stone} algebras},
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Inigo Incer. An adjunction between boolean algebras and a subcategory of Stone algebras. Theory and applications of categories, Tome 41 (2024), pp. 2041-2057. http://geodesic.mathdoc.fr/item/TAC_2024_41_a56/