Abstract
In this art cle I give the de .n t on of the strong and weak re .ex v ty and the com- pat bility relation of objects in a categorical language.These concepts will generalize the corresponding concepts n the theory of topolog cal vector spaces. The main theorem makes clear the connection between these mportant concepts and we can show a lot of objects in our category,which are not strongly re .exive,but compatible with strongly re .ex ve objects.We also consider a lot of interesting examples and try to throw new light upon the ex stence of such Abelian groups which satisfy Pontryagin duality but do not respect compactness.We w ll prove also that the weak topolog cal vector space- structures are not re .ex ve in general.
Published Version
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