Displaying similar documents to “Extensional subobjects in categories of Ω -fuzzy sets”

Complete subobjects of fuzzy sets over M V -algebras

Jiří Močkoř (2004)

Czechoslovak Mathematical Journal

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A subobjects structure of the category Ω - of Ω -fuzzy sets over a complete M V -algebra Ω = ( L , ∧ , ∨ , ⊗ , → ) is investigated, where an Ω -fuzzy set is a pair 𝐀 = ( A , δ ) such that A is a set and δ A × A → Ω is a special map. Special subobjects (called complete) of an Ω -fuzzy set 𝐀 which can be identified with some characteristic morphisms 𝐀 → Ω * = ( L × L , μ ) are then investigated. It is proved that some truth-valued morphisms ¬ Ω Ω * → Ω * , ∩ Ω , ∪ Ω Ω * × Ω * → Ω * are characteristic morphisms of complete subobjects.

Some notes on the category of fuzzy implications on bounded lattices

Amin Yousefi, Mashaallah Mashinchi, Radko Mesiar (2021)

Kybernetika

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In this paper, we introduce the product, coproduct, equalizer and coequalizer notions on the category of fuzzy implications on a bounded lattice that results in the existence of the limit, pullback, colimit and pushout. Also isomorphism, monic and epic are introduced in this category. Then a subcategory of this category, called the skeleton, is studied. Where none of any two fuzzy implications are Φ -conjugate.

Information systems in categories of valued relations.

Vladimir B. Gisin (1994)

Mathware and Soft Computing

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The paper presents a categorical version of the notion of information system due to D. Scott. The notion of information system is determined in the framework of ordered categories with involution and division and the category of information systems is constructed. The essential role in all definitions and constructions play correlations between inclusion relations and entailment relations.

On corings and comodules

Hans-Eberhard Porst (2006)

Archivum Mathematicum

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It is shown that the categories of R -coalgebras for a commutative unital ring R and the category of A -corings for some R -algebra A as well as their respective categories of comodules are locally presentable.