Limits in Modified Categories of Interest

Abstract

We firstly prove the completeness of the category of crossed modules in a modified category of interest. Afterwards, we define pullback crossed modules and pullback cat${}^1$-objects that are both obtained by pullback diagrams with extra structures on certain arrows. These constructions unify many corresponding results for the cases of groups, commutative algebras and can also be adapted to various algebraic structures.

17 pages, to appear in Bulletin of the Iranian Mathematical Society