On categories of quantale valued sets

José Goudet Alvim; Caio de Andrade Mendes; Hugo Luiz Mariano

Published

2024-01-22

On categories of quantale valued sets

Sobre Categorías de Conjuntos Quantale-Valuados

Keywords:

quantales, categories, fuzzy-sets (en)
quantales, categorias, conjuntos difusos (es)

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Authors

José Goudet Alvim University of Sao Paulo
Caio de Andrade Mendes University of Sao Paulo
Hugo Luiz Mariano University of Sao Paulo

Abstract (en)
Abstract (es)

We introduce and study some categories of quantale valued sets defined over commutative semicartesian quantales (quantales "with projections"). This extends known results on locale valued sets and establishes a preliminary categorial step to deal with internal logic of such categories.

Introducimos y estudiamos algunas categorías de conjuntos valuados por quantales semicartesianos conmutativos (quantales "con proyecciones"). Esto amplía los resultados conocidos sobre conjuntos valuados localmente y establece un paso categorial preliminar para tratar con la lógica interna de tales categorías.

References

Jirí Adámek and Jirí Rosicky, Locally presentable and accessible categories, vol. 189, Cambridge University Press, 1994.

José Goudet Alvim, Caio de Andrade Mendes, and Hugo Luiz Mariano, Q-sets and friends: Categorical constructions and categorical properties, arXiv (2023), no. 2302.03123.

José Goudet Alvim, Caio de Andrade Mendes, and Hugo Luiz Mariano, Q-sets and friends: Regarding singleton and gluing completeness, arXiv (2023), no. 2302.03691.

Francis Borceux, Handbook of Categorical Algebra: Volume 3, Sheaf Theory. Encyclopedia of Mathematics and its Applications, Cambridge University Press, 1994.

C. C. Chang, Algebraic analysis of many valued logics, Transactions of the American Mathematical Society 88 (1958), 467-490.

Marcelo E. Coniglio and Francisco Miraglia, Non-commutative topology and quantales, Studia Logica 65 (2000), no. 2, 223-236.

Michael Fourman and Dana Scott, Sheaves and Logic, LNM: Applications of sheaves 753 (1979), 302-401.

Ulrich Hohle, Monoidal closed categories, weak topoi and generalized logics, Fuzzy Sets and Systems 42 (1991), 15-35.

Francisco Miraglia and Ugo Solitro, Sheaves over right sided idempotent quantales, Logic Journal of IGPL 6 (1998), no. 4, 545-600.

Ana Luiza Tenório, Caio de Andrade Mendes, and Hugo Luiz Mariano, On sheaves on semicartesian quantales and their truth values, arXiv (2023), no. 2204.08351 v2.

How to Cite

APA

Alvim, J. G., Mendes, C. de A. and Mariano, H. L. (2023). On categories of quantale valued sets. Boletín de Matemáticas, 30(2), 41–47. https://revistas.unal.edu.co/index.php/bolma/article/view/112590

ACM

[1]

Alvim, J.G., Mendes, C. de A. and Mariano, H.L. 2023. On categories of quantale valued sets. Boletín de Matemáticas. 30, 2 (Oct. 2023), 41–47.

ACS

(1)

Alvim, J. G.; Mendes, C. de A.; Mariano, H. L. On categories of quantale valued sets. Bol. Matemáticas 2023, 30, 41-47.

ABNT

ALVIM, J. G.; MENDES, C. de A.; MARIANO, H. L. On categories of quantale valued sets. Boletín de Matemáticas, [S. l.], v. 30, n. 2, p. 41–47, 2023. Disponível em: https://revistas.unal.edu.co/index.php/bolma/article/view/112590. Acesso em: 28 apr. 2025.

Chicago

Alvim, José Goudet, Caio de Andrade Mendes, and Hugo Luiz Mariano. 2023. “On categories of quantale valued sets”. Boletín De Matemáticas 30 (2):41-47. https://revistas.unal.edu.co/index.php/bolma/article/view/112590.

Harvard

Alvim, J. G., Mendes, C. de A. and Mariano, H. L. (2023) “On categories of quantale valued sets”, Boletín de Matemáticas, 30(2), pp. 41–47. Available at: https://revistas.unal.edu.co/index.php/bolma/article/view/112590 (Accessed: 28 April 2025).

IEEE

[1]

J. G. Alvim, C. de A. Mendes, and H. L. Mariano, “On categories of quantale valued sets”, Bol. Matemáticas, vol. 30, no. 2, pp. 41–47, Oct. 2023.

MLA

Alvim, J. G., C. de A. Mendes, and H. L. Mariano. “On categories of quantale valued sets”. Boletín de Matemáticas, vol. 30, no. 2, Oct. 2023, pp. 41-47, https://revistas.unal.edu.co/index.php/bolma/article/view/112590.

Turabian

Alvim, José Goudet, Caio de Andrade Mendes, and Hugo Luiz Mariano. “On categories of quantale valued sets”. Boletín de Matemáticas 30, no. 2 (October 11, 2023): 41–47. Accessed April 28, 2025. https://revistas.unal.edu.co/index.php/bolma/article/view/112590.

Vancouver

1.

Alvim JG, Mendes C de A, Mariano HL. On categories of quantale valued sets. Bol. Matemáticas [Internet]. 2023 Oct. 11 [cited 2025 Apr. 28];30(2):41-7. Available from: https://revistas.unal.edu.co/index.php/bolma/article/view/112590