Colimits of crossed modules in modified categories of interest

Abstract

In this paper, we give the constructions of the coequalizer and coproduct objects for the category of crossed modules, in a modified category of interest (MCI). In other words, we prove that the corresponding category is finitely cocomplete.

Some Remarks on MCI Crossed Modules

“…all codomains are fixed [8]. Furthermore, the cocompleteness has been studied in [3]. In this paper, we prove that we also have the same completeness property without any restriction neither on domains nor on codomains.…”