Further criteria for totality. (English) Zbl 0626.18001

This paper gives a result missed by G. M. Kelly in his survey paper [ibid. 27, 109-132 (1986; Zbl 0593.18007)]: if a category is cocomplete, admits arbitrary cointersections of epics and has a small generating set, then it is total. Recent work of R. Börger and W. Tholen has provided several counterexamples in this area.
Reviewer: R.Street


18A35 Categories admitting limits (complete categories), functors preserving limits, completions
18A32 Factorization systems, substructures, quotient structures, congruences, amalgams


Zbl 0593.18007
Full Text: Numdam EuDML


[1] 1 B.J. Day , On adjoint-functor factorization , Lecture Notes in Math , 420 , Springer ( 1974 ), 1 - 19 , MR 396717 | Zbl 0367.18004 · Zbl 0367.18004
[2] 2, G.M. Kelly , A survey of totality for enriched and ordinary categories , Cahiers Top et Géom, Diff , XXVII - 2 ( 1986 ), 109 - 132 (and references therein), Numdam | MR 850527 | Zbl 0593.18007 · Zbl 0593.18007
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