Main Article Content
Disconnectedness Classes
Abstract
Let χ be an (E, M)-category for sinks.
A notion of disconnectedness with respect to a closure operator C on χ and
to a class of χ-monomorphisms N is introduced. This gives
rise to the notion of N-disconnectedness class, a characterization
of which is presented in a category with a terminal object. Some examples are
provided.
Mathematics Subject Classification (1991): 18A32, 06A15, 18E40
Keywords: closure operator, disconnectedness, Galois connection, constant
morphism, torsion theories, radicals, factorization of morphisms, substructures,
quotient structures, congruences, amalgams, Galois correspondences, closure
operators, sink, category, categories, terminal object
Quaestiones Mathematicae
24(1) 2001, 75–92
A notion of disconnectedness with respect to a closure operator C on χ and
to a class of χ-monomorphisms N is introduced. This gives
rise to the notion of N-disconnectedness class, a characterization
of which is presented in a category with a terminal object. Some examples are
provided.
Mathematics Subject Classification (1991): 18A32, 06A15, 18E40
Keywords: closure operator, disconnectedness, Galois connection, constant
morphism, torsion theories, radicals, factorization of morphisms, substructures,
quotient structures, congruences, amalgams, Galois correspondences, closure
operators, sink, category, categories, terminal object
Quaestiones Mathematicae
24(1) 2001, 75–92
