Algebraic Properties of Category of Involutive M-Semilattices and Its Limits
Shaohui Liang · Preprints.org · 2025
In this paper, firstly, the concepts of nucleus and congruence are introduced in involutive m-semilattices, and their interrelationships are discussed. On this basis, the concrete structure of coequalizer in the category of involutive m-semilattices is obtained. We introduce the definition of the free involutive m-semilattices, and concrete structure of the involutive m-semilattices is discussed, and in addition, we prove that the category of involutive m-semilattices is algebraic. Scondly, the colimit in the category of involutive m-semilattices is a very difficult problem. We have obtained the concrete structure of colimit for a full subcategory of the category of involutive m-semilattices. Thirdly, we introduced the definition of an inverse system in the category of involutive m-semilattices, and give the concrete structure of the inverse limit of an inverse system. We establish the concept of a mapping between two inverse systems. The properties between inverse limits are discussed. Finally, we study the direct limit of the category of involutive m-semilattices and give its concrete structure.