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The existence of abelian categories with a finite number of objects or with finite Homs is investigated. Thus a complete characterization of categories having a finite number of objects and morphisms, with products and a zero-object, is given. The non existence of abelian categories with a finite number of objects, non finite Hom and with endomorphisms satisfying the following condition is then proved: every endomorphismis a mono-epimorphism. An example of abelian category with a unique non zero-object...
In this paper we prove that any incidence-preserving bijection between the line sets of Grassmann spaces is induced by either a collineation or a correlation.
In the present paper, following a previous one by the same Authors [2], we state a sufficient condition for the existence of kernels for homomorphisms between inversive semigroups in an abstract category.
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