Definable completeness. (English) Zbl 1067.18001
In a series of joint papers with J. Funk, the first author has developed the topos-theoretic analogue of R. H. Fox’s topological notion of complete spread. The goal of the present paper is to separate out the spread property from the completeness: the authors introduce a notion of ‘definable completeness’ for geometric morphisms, and prove that a geometric morphism with locally connected domain and bounded codomain is definably complete (resp.a spread) iff the pure part of its comprehensive factorization is a surjection (resp.an inclusion).
Reviewer: Peter T. Johnstone (Cambridge)
References:
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