Karimi Feizabadi, A. (2019). The categories of lattice-valued maps, equalities, free objects, and $\mathcal C$-reticulation. Categories and General Algebraic Structures with Applications, 11(Special Issue Dedicated to Prof. George A. Grätzer), 93-112.

Abolghasem Karimi Feizabadi. "The categories of lattice-valued maps, equalities, free objects, and $\mathcal C$-reticulation". Categories and General Algebraic Structures with Applications, 11, Special Issue Dedicated to Prof. George A. Grätzer, 2019, 93-112.

Karimi Feizabadi, A. (2019). 'The categories of lattice-valued maps, equalities, free objects, and $\mathcal C$-reticulation', Categories and General Algebraic Structures with Applications, 11(Special Issue Dedicated to Prof. George A. Grätzer), pp. 93-112.

Karimi Feizabadi, A. The categories of lattice-valued maps, equalities, free objects, and $\mathcal C$-reticulation. Categories and General Algebraic Structures with Applications, 2019; 11(Special Issue Dedicated to Prof. George A. Grätzer): 93-112.

The categories of lattice-valued maps, equalities, free objects, and $\mathcal C$-reticulation

^{}Department of Mathematics, Gorgan Branch, Islamic Azad University, Gorgan, Iran.

Abstract

In this paper, we study the concept of $\mathcal C$-reticulation for the category $\mathcal C$ whose objects are lattice-valued maps. The relation between the free objects in $\mathcal C$ and the $\mathcal C$-reticulation of rings and modules is discussed. Also, a method to construct $\mathcal C$-reticulation is presented, in the case where $\mathcal C$ is equational. Some relations between the concepts reticulation and satisfying equalities and inequalities are studied.

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