Results 121 to 130 of about 576 (163)
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Quantale algebras as lattice-valued quantales
Soft Computing, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bin Zhao
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Quantale-valued dissimilarity [PDF]
Fuzzy Sets and Systems, 2020 Inspired by the theory of apartness relations of Scott, we establish a positive theory of dissimilarity valued in an involutive quantale $\mathsf{Q}$ without the aid of negation. It is demonstrated that a set equipped with a $\mathsf{Q}$-valued dissimilarity is precisely a symmetric category enriched in a subquantaloid of the quantaloid of back ...
Hongliang Lai, Lili Shen, Dexue Zhang
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Mathematica Slovaca, 2023
Abstract In this paper, we study the enlargements of quantales. We prove three main results. First, if Q is a factorizable quantale, then any matrix quantale over Q is an enlargement of Q; second, any unital Rees matrix quantale over a quantale Q with an identity is an enlargement of Q; third, two quantales are Morita ...
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Abstract In this paper, we study the enlargements of quantales. We prove three main results. First, if Q is a factorizable quantale, then any matrix quantale over Q is an enlargement of Q; second, any unital Rees matrix quantale over a quantale Q with an identity is an enlargement of Q; third, two quantales are Morita ...
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Information Sciences, 2013
Rough set theory is a useful mathematical tool for dealing with the uncertainty and granularity in information systems. In this paper, rough approximations are introduced into quantales, a kind of partially ordered algebraic structure with an associative binary multiplication.
Lingyun Yang, Luoshan Xu
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Rough set theory is a useful mathematical tool for dealing with the uncertainty and granularity in information systems. In this paper, rough approximations are introduced into quantales, a kind of partially ordered algebraic structure with an associative binary multiplication.
Lingyun Yang, Luoshan Xu
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The powerset monad on quantale-valued sets [PDF]
Fuzzy Sets and SystemsFor a small involutive quantaloid $\mathcal{Q}$, it is shown that the category of separated complete $\mathcal{Q}$-categories and left adjoint $\mathcal{Q}$-functors is strictly monadic over the category of symmetric $\mathcal{Q}$-categories.
Lili Shen, Xiaojuan Zhao
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1995
In this paper, we investigate the ideas involved in extending to the non-commutative case the concepts of presheaf and sheaf on a locale. The context within which we shall work will be that of quantales, introduced by the first author [10, 11] to provide a framework for the development of the Gelfand representation of not necessarily commutative C ...
C. J. Mulvey, M. Nawaz
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In this paper, we investigate the ideas involved in extending to the non-commutative case the concepts of presheaf and sheaf on a locale. The context within which we shall work will be that of quantales, introduced by the first author [10, 11] to provide a framework for the development of the Gelfand representation of not necessarily commutative C ...
C. J. Mulvey, M. Nawaz
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Applied Categorical Structures, 2002
The paper gives an appropriate notion of a prime element of a quantale and characterizes spatial quantales as those quantales having enough primes. This result solves a problem stated by \textit{J. W. Pelletier} and the reviewer [``Simple involutive quantales'', J. Algebra 195, 367-386 (1997; Zbl 0894.06005)].
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The paper gives an appropriate notion of a prime element of a quantale and characterizes spatial quantales as those quantales having enough primes. This result solves a problem stated by \textit{J. W. Pelletier} and the reviewer [``Simple involutive quantales'', J. Algebra 195, 367-386 (1997; Zbl 0894.06005)].
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Frobenius Quantales, Serre Quantales and the Riemann–Roch Theorem
Studia Logica, 2021\par A quantale \(Q\) is a \(\bigvee\)-semilattice equipped with an associative binary operation \(\otimes:Q\times Q\rightarrow Q\) distributing over \(\bigvee\) from both sides, i.e., \(a\otimes(\bigvee S)=\bigvee_{s\in S}(a\otimes s)\) and \((\bigvee S)\otimes a=\bigvee_{s\in S}(s\otimes a)\) for every \(a\in Q\) and every \(S\subseteq Q\).
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Applied Categorical Structures, 2003
The author introduces distributive quantales and shows that (a) every spatial quantale is distributive and (b) every algebraic distributive quantale is spatial.
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The author introduces distributive quantales and shows that (a) every spatial quantale is distributive and (b) every algebraic distributive quantale is spatial.
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Sheaves on involutive quantales: Grothendieck quantales
Fuzzy Sets and Systems, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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