The category of L-algebras

Abstract

‎In this paper‎, ‎we define and study the category of L-algebras‎, ‎proving that this category has equalizers‎, ‎coequalizers‎, ‎kernel pairs and products‎. ‎We investigate the existence of injective objects in this category‎ ‎and show that an object in the subcategory of cyclic L-algebras is injective if and only if it is a complete and divisible cyclic L-algebra‎.

Keywords

• l-algebra‎
• ‎cyclic l-algebra‎
• ‎mv-algebra‎
• ‎equalizer‎
• ‎product‎
• co-product‎