TY - JOUR ID - 87118 TI - The categories of lattice-valued maps, equalities, free objects, and $\mathcal C$-reticulation JO - Categories and General Algebraic Structures with Applications JA - CGASA LA - en SN - 2345-5853 AU - Karimi Feizabadi, Abolghasem AD - Department of Mathematics, Gorgan Branch, Islamic Azad University, Gorgan, Iran. Y1 - 2019 PY - 2019 VL - 11 IS - Special Issue Dedicated to Prof. George A. Grätzer SP - 93 EP - 112 KW - Free object KW - $ell$-ring KW - $ell$-module KW - frame KW - cozero map KW - semi-cozero map KW - the $F$-Zariski topology KW - $mathcal C$-reticulation KW - lattice-valued map DO - 10.29252/cgasa.11.1.93 N2 - 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. UR - https://cgasa.sbu.ac.ir/article_87118.html L1 - https://cgasa.sbu.ac.ir/article_87118_fdc1919782d40300997d11b44b33109b.pdf ER -