A~universal property of Deheuvels homology

E. M. Beniaminov

Sbornik. Mathematics, Tome 13 (1971) no. 1, pp. 65-79

Résumé

This paper gives a construction leading to Deheuvels homology of compact metric spaces with coefficients in copresheaves of abelian groups. We construct an epimorphic map of Deheuvels homology onto Aleksandrov–Čech homology, whose kernel is expressed in terms of the derived functors of the inverse limit functor. We consider projective objects in the category of copresheaves of abelian groups and homology with coefficients in projective copresheaves. The fundamental result of the paper is the theorem that the Deheuvels homology of compact metric spaces with coefficients in copresheaves of abelian groups is a universal extension of Aleksandrov–Čech homology among homologies which satisfy the exactness condition and other natural requirements. Bibliography: 5 titles.