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Effective descent morphisms and effective equivalence relations. (English) Zbl 0792.18002

Seely, R. A. G. (ed.), Category theory 1991. Proceedings of an international summer category theory meeting, held in Montréal, Québec, Canada, June 23-30, 1991. Providence, RI: American Mathematical Society. CMS Conf. Proc. 13, 421-433 (1992).
In categories with pullbacks and coequalizers, a characterization of effective descent morphisms is given in terms of effectiveness of some equivalence relations and universality of their coequalizers. The stability of the class of effective descent morphisms under pullbacks is proved, and stability under composition is investigated.
For the entire collection see [Zbl 0771.00047].

MSC:

18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphisms
18C20 Eilenberg-Moore and Kleisli constructions for monads
18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)
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