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Factorizations, fibres and connectedness. (English) Zbl 0547.18001
Categorical topology, Proc. int. Conf., Toledo/Ohio 1983, Sigma Ser. Pure Math. 5, 549-566 (1984).
[For the entire collection see Zbl 0543.00008.]
The title lists the principal characters in a rather drastic extension of abstract connectedness theory. If topological spaces have torsion, certainly groups must have connectedness. Roughly, constants in a category of groups must be zero, so a map has only one fibre, its kernel; but that is enough for many purposes. The aim seems to be more directly at categorical topology in a topos. All the theorems are more or less grammatical.
Reviewer: J.R.Isbell

18B30 Categories of topological spaces and continuous mappings (MSC2010)
54B30 Categorical methods in general topology
18E40 Torsion theories, radicals
18B25 Topoi
18D99 Categorical structures