The monad of inclusion hyperspaces and its algebras

Adjoints and Monads Related to Compact Lattices and Compact Lawson Idempotent Semimodules

“…For any subset A ⊂ exp X its transversal [13] A ⊥ = {B ∈ exp X | B ∩ A = ∅ for all A ∈ A} is closed, and, for closed A, the correspondence A → A ⊥ is continuous as a mapping exp(exp X) → exp(exp X) and antitone (with respect to inclusion).…”

Idempotent Convexity and Algebras for the Capacity Monad and its Submonads

“…Theorem 2 [15] states that for a G-algebra (X, θ) the operations ⊕ : X × X → X, ⊗ : I × X → X defined by the formulae x ⊕ y = θ(η G X(x) ∩ η G X(y)) and x ⊗ y = θ(η G X(x) ∪ η G X(y)) are such that (X, ⊕, ⊗) is a Lawson lattice. We apply this theorem to θ = ξ • i G X and obtain that X with the operations x ⊕ y = ξ(δ x ∨ δ y ) and x ⊗ y = ξ(δ x ∧ δ y ) is a Lawson lattice.…”

“…Zarichnyi [20] has shown that the category of algebras for the superextension monad is isomorphic to the category of compacta with (fixed) almost normal T 2 -subbase and their convex maps. We will use a result of Radul [15] who introduced the inclusion hyperspace triple and proved that its algebras and their morphisms are in fact compact Lawson lattices and their complete homomorphisms.…”

Функтор Емкостей В Категории Компактов

“…Монада G, порожденная функтором G, описана в [11]. Умножение µ G : [16]) называем естественное преобразование ϕ :…”

“…В статье установлена тесная связь между монадой емкостей и монадой гиперпространств включения, определенной Т. Радулом [11]; описано вложение второй монады в первую и получен класс монад, занимающих промежуточное положение и аппроксимирующих монаду емкостей.…”