Published online by Cambridge University Press: 22 January 2016
The aim of this paper is to investigate some applications of a certain universal problem. The universal problem deals with categories C which for every object A have some ‘‘structure” on the set C(A, A) of endomorphisms of A and calls for a universal solution, relative to this structure, that is associated with C(A, A) and centralizes the set of automorphisms of A. The commutative version of this universal problem asks for a universal solution, relative to the said structure, that abelianizes the canonical monoid structure of C(A, A).