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On the Category of Quantale-Semimodules

  • M. K. Dubey
  • Vijay K. Yadav
  • S. P. Tiwari
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 714)

Abstract

The concepts from quantale theory is applied in this work to bring forward and study an abstract idea of quantale-semimodule (Q-semimodule) and Q-sets. We have introduced the category \(\varvec{Q}\)-Mod of Q-semimodule and confer an adjunction between the category \(\varvec{Q}\)-Mod and the well-known category Set, and another between the category \(\varvec{L}\)-Set of L-sets and the category \(\varvec{Q}\)-Set of Q-sets. Finally, we have shown that the category \(\varvec{Q}\)-Mod forms a monoidal category.

Keywords

Quantale Q-semimodule Morphism Category 

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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of Applied MathematicsIndian Institute of Technology (Indian School of Mines)DhanbadIndia
  2. 2.Department of Mathematics, School of Mathematics, Statistics and Computational SciencesCentral University of RajasthanBandar Sindari, AjmerIndia

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