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

Document Type : Research Paper


Department of Mathematics, Gorgan Branch, Islamic Azad University, Gorgan, Iran.



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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