Category theoretic aspects of chain-valued frames. I: Categorical and presheaf theoretic foundations

DOI10.1016/J.FSS.2007.07.010zbMath1170.18004OpenAlexW1973002978MaRDI QIDQ834493

Ales Pultr, Stephen E. Rodabaugh

Publication date: 26 August 2009

Published in: Fuzzy Sets and Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.fss.2007.07.010

zbMATH Keywords

completenesscocompleteness\(L\)-frames\(L\)-frm\(L\)-loc\(L\)-top\(L\)-topological spacesanti-stratified/stratified spacescharacteristic/Martin/stratification functorsfactorization structuresimage/preimage operatorsiota/omega functorsspectrum functorsuniversal/co-universal spacesupper/lower forgetful functorsupper/lower free functors

Mathematics Subject Classification ID

Categorical methods in general topology (54B30)

Related Items (24)

Fundamental duality of abstract categories and its applications ⋮ Category theoretic aspects of chain-valued frames. II: Applications to lattice-valued topology ⋮ Uniform-type structures on lattice-valued spaces and frames ⋮ Sobriety and spatiality in varieties of algebras ⋮ Bounded sobriety and k-bounded sobriety of Q-cotopological spaces ⋮ On fuzzy monotone convergence \(\mathcal{Q}\)-cotopological spaces ⋮ Overview and comparison of localic and fixed-basis topological products ⋮ Hypergraph functor and attachment ⋮ A survey of fuzzifications of frames, the Papert-Papert-Isbell adjunction and sobriety ⋮ Category-theoretic fuzzy topological spaces and their dualities ⋮ An approach to fuzzy frames via fuzzy posets ⋮ On the uniformization of lattice-valued frames ⋮ Composite variety-based topological theories ⋮ Sobriety and spatiality in categories of lattice-valued algebras ⋮ A note on \(\alpha \)- and \(\alpha ^{*}\)-Hausdorffness ⋮ Fuzzy uniform structures and continuous t-norms ⋮ On lattice-valued frames: the completely distributive case ⋮ Necessity of non-stratified and anti-stratified spaces in lattice-valued topology ⋮ From quantale algebroids to topological spaces: fixed- and variable-basis approaches ⋮ Fuzzy algebras as a framework for fuzzy topology ⋮ Generalized fuzzy topology versus non-commutative topology ⋮ Variable-basis topological systems versus variable-basis topological spaces ⋮ Sobriety of quantale-valued cotopological spaces ⋮ On ordered categories as a framework for fuzzification of algebraic and topological structures

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