The categories of lattice-valued maps, Equalities, Free objects, and $mathcal C$-reticulation
Abolghasem Karimi Feizabadi · Categories and General Algebraic Structures with Application · 2019
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.