Algebraic and Categorical Aspects of Quantales

DOI10.1016/S1570-7954(07)05006-1zbMath1219.06016MaRDI QIDQ3053874

Jan Paseka, David Kruml

Publication date: 30 October 2010

Published in: Handbook of Algebra (Search for Journal in Brave)

zbMATH Keywords

survey paperquantales

Mathematics Subject Classification ID

Quantales (06F07)

Related Items (63)

Free \(Q\)-algebras. ⋮ Quantale-valued sup-algebras ⋮ On the power-set \(Q\)-algebras ⋮ The unitality of quantum B-algebras ⋮ Injective hulls for ordered algebras ⋮ A note on the number of subquantales ⋮ Sierpinski object for affine systems ⋮ Lattice-valued topological systems as a framework for lattice-valued formal concept analysis ⋮ Coproduct and amalgamation of deductive systems by means of ordered algebras ⋮ Non-commutative logical algebras and algebraic quantales ⋮ Distributivity and residuation for lexicographic orders ⋮ Lattice-valued soft algebras. ⋮ Prime elements of non-integral quantales and their applications. ⋮ Unnamed Item ⋮ Reflectors to quantales ⋮ Sierpinski object for composite affine spaces ⋮ Constructing \(Q\)-algebras from \(Q\)-modules ⋮ On the cancellation problem for quantales ⋮ Unitless Frobenius quantales ⋮ Quantum B‐modules ⋮ On limits and colimits of variety-based topological systems ⋮ On a generalization of the concept of state property system ⋮ The quantale of order-preserving maps of a completely distributive lattice ⋮ A survey of fuzzifications of frames, the Papert-Papert-Isbell adjunction and sobriety ⋮ Categorical foundations of variety-based topology and topological systems ⋮ Quantale algebras as lattice-valued quantales ⋮ Quotients and colimits of \(\kappa \)-quantales ⋮ Remark on the unital quantale \(Q[e\)] ⋮ Generalized approximations of \(( \in ,\in \vee q) \)-fuzzy ideals in quantales ⋮ Categorically algebraic topology versus universal topology ⋮ Unnamed Item ⋮ Representation theorems for \(Q\)-algebras ⋮ On categorical aspects of \(S\)-quantales ⋮ K-FLAT PROJECTIVE FUZZY QUANTALES ⋮ The MacNeille completions for residuated \(S\)-posets ⋮ Free and cofree \(S\)-quantales ⋮ Epimorphisms of \(S\)-quantales ⋮ Composite variety-based topological theories ⋮ From quantale algebroids to topological spaces: fixed- and variable-basis approaches ⋮ Girard couples of quantales ⋮ On the quantale of quantic nuclei ⋮ Fuzzy algebras as a framework for fuzzy topology ⋮ Generalized fuzzy topology versus non-commutative topology ⋮ Nuclei and conuclei on residuated lattices ⋮ Value semigroups, value quantales, and positivity domains ⋮ Some further results on free quantale algebras ⋮ Unnamed Item ⋮ CHARACTERIZATION OF PROJECTIVE QUANTALES ⋮ Characterization of a category for monoidal topology ⋮ Generalized approximation of substructures in quantales by soft relations ⋮ Many for the price of one duality principle for affine sets ⋮ Residuation for soft constraints: lexicographic orders and approximation techniques ⋮ Some studies in the approximation of \((\in_\gamma, \in_\gamma \vee q_\delta)\)-fuzzy substructures in quantales ⋮ Enriched topologies and topological representation of semi-unital and semi-integral quantales ⋮ On the coextension of cut-continuous pomonoids ⋮ Extended-order algebras as a generalization of posets ⋮ Dual quantum B-algebras ⋮ On the injective hulls of quantum B-algebras ⋮ On injective constructions of \(S\)-semigroups ⋮ Moore-Penrose equations in involutive residuated semigroups and involutive quantales ⋮ Another look on tense and related operators ⋮ On a lax-algebraic characterization of closed maps ⋮ On fuzzification of topological categories

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