PRESERVING INJECTIVE PROPERTIES OF ACTS OVER MONOIDS UNDER LIMITS AND THEIR TRANSFER FROM COLIMITS TO THE COMPONENTS

Abstract

This paper is devoted to the preservation of injective properties under limits and their transfer from colimits to the components.  We prove that an injective property α is preserved under limits if and only if all acts satisfy property α.  Besides we prove that an injective property α is transferred from colimits to their components if and only if all acts satisfy property α.