Strongly Hopfian and Strongly Cohopfian Objects in the Category of Complexes of Left $A$-Modules

Abstract

The object of this paper is the study of strongly hopfian, strongly cohopfian, quasi-injective, quasi-projective, Fitting objects of the category of complexes of A-modules. In this paper we demonstrate the following results: a)If C is a strongly hopfian chain complex (respectively strongly cohopfian chain complex) and E a subcomplex which is direct summand then E and C/E are both strongly Hopfian (respectively strongly coHopfian) then C is strongly Hopfian (respectively strongly coHopfian). b)Given a chain complex C, if C is quasi-injective and strongly-hopfian then C is strongly cohopfian.